Previous seminars

Monday 15th December: Christian Brennecke (University of Bonn)

On the Leading Order Term of the Lattice Yang-Mills Free Energy

Abstract:  In a recent paper, S. Chatterjee determined the leading order term of the free energy of U(N) lattice Yang-Mills theory in $\Lambda_n=\{0,\ldots,n\}^d\subset \bZ^d$, for every $N\geq 1$ and $d\geq 2$. The formula is explicit apart from a contribution $K_d$ which corresponds to the limiting free energy of lattice Maxwell theory with boundary conditions induced by the axial gauge. After a brief motivation, I recall some of the key steps to obtain the leading order term of the free energy and I explain an equivalent characterization of $K_d$ that admits its explicit computation, for every $d\geq 2$.  

Tuesday 9th December, room 8-02 at 16:15: Beatrice Costeri (Università di Pavia)

A microlocal approach to the stochastic nonlinear Dirac equation 

Abstract: We present a novel framework for the study of a wide class of nonlinear Fermionic stochastic partial differential equations of Dirac type, which is inspired by the functional approach to the λ Φ^3 model. The main merit is that, by realizing random spinor fields within a suitable algebra of functional-valued Dirac distributions, we are able to use specific techniques proper of microlocal analysis. These allow us to deal with renormalization using an Epstein-Glaser perspective, hence without resorting to any specific regularization scheme. As a concrete example we shall use this method to discuss the stochastic Thirring model in two Euclidean dimensions and we shall comment on its applicability to a larger class of Fermionic SPDEs.

Based on joint work with A. Bonicelli, C. Dappiaggi and P. Rinaldi -- Math.Phys.Anal.Geom. 27 (2024) 3, 16

Monday 8th December: Claudio Dappiaggi (Università di Pavia)

Stochastic Partial Differential Equations and Renormalization à la Epstein-Glaser

Abstract: We present a novel framework for the study of a large class of nonlinear stochastic partial differential equations, which is inspired by the algebraic approach to quantum field theory. The main merit is that, by realizing random fields within a suitable algebra of functional-valued distributions, we are able to use specific techniques proper of microlocal analysis. These allow us to deal with renormalization using an Epstein-Glaser perspective, hence without resorting to any specific regularization scheme.  As a concrete example we shall use this method to discuss the stochastic $\Phi^3_d$ model and we shall comment on its applicability to the stochastic nonlinear Schrödinger equation as well as to the stochastic Thirring model -- Joint works with Alberto Bonicelli, Beatrice Costeri,  Nicolò Drago, Paolo Rinaldi and Lorenzo Zambotti.

Monday 1st of December: Alexander Drewitz (Universität zu Köln)

Branching Processes and the Fisher–KPP Equation in Spatially Random Environments

Abstract: Branching Brownian motion, branching random walks, and the Fisher–KPP equation have been central objects of study in probability theory and mathematical physics over the past decades. Through the Feynman–Kac and McKean representations, the behavior of extremal particles in the branching models is intimately linked to the position of the traveling wave front in the Fisher–KPP equation.

In this talk, I will present recent progress on extensions of these classical models to spatially random environments, incorporating random branching rates and random nonlinearities. It turns out that such inhomogeneities give rise to a significantly richer and more delicate phenomenology than in the homogeneous case.

Monday 24th of November: Paul Dario (CY Cergy Paris Université)

Parallel spin wave for the Villain model

Abstract: This talk will focus on the decay of correlations in the Villain model. We consider the low-temperature regime in dimensions d>3, where it is conjectured that the cosine-cosine correlation between two spins decays like the inverse of their distance to the power 2(d-2). The work of Bricmont, Fontaine, Lebowitz, Lieb, and Spencer (1982) shows that this correlation decays at least as fast as the inverse distance to the power d-2. I will present a recent result that improves this bound to an exponent of d-1, up to a logarithmic correction.

The proof builds on a key insight of Fröhlich and Spencer (1982): at low temperature, a duality transformation combined with a renormalisation argument can be used to map the Villain model to a variant of the well-studied \nabla\phi interface model. This latter model can then be analysed precisely using the Helffer–Sjöstrand formula together with elliptic regularity estimates.

Joint work with W. Wu.

Monday 17th of November: Michele Salvi (University of Rome “Tor Vergata”)

Random Spanning Trees in Random Environment

Abstract: A spanning tree of a graph G is a connected subset of G without cycles. The Uniform Spanning Tree (UST) is obtained by choosing one of the possible spanning trees of G at random. The Minimum Spanning Tree (MST) is realised instead by putting random weights on the edges of G and then selecting the spanning tree with the smallest weight. These two models exhibit markedly different behaviours: for example, their diameter on the complete graph with n nodes transitions from n^1/2 for the UST to n^1/3 for the MST. 

What lies in between? 

We introduce a model of Random Spanning Trees in Random Environment (RSTRE) designed to interpolate between UST and MST. In particular, when the environment disorder is sufficiently low, the RSTRE on the complete graph has a diameter of n^1/2 as the UST. Conversely, when the disorder is high, the diameter behaves like n^1/3 as for the MST. We conjecture a smooth transition between these two values for intermediate levels of disorder.

This talk is based on joint work with Rongfeng Sun and Luca Makowiec (NUS Singapore).

Monday 10th of November: Cyril Labbé (LPSM, Paris Cité)

Construction and spectrum of the Schrodinger operator with white noise potential

Abstract: This talk will focus on the random Schrodinger operator obtained by perturbing the Laplacian on R^2 and R^3 by a white noise. This is a singular operator and one needs to renormalize it using recent tools from stochastic PDEs. I will give a brief review of the literature on this operator, and I will present a result on the identification of its almost sure spectrum. Based on a joint work with Yueh-Sheng Hsu (TU Wien).

Monday 3rd of November: Justin Salez (Université Paris-Dauphine & PSL)

An invitation to the cutoff phenomenon

Abstract: The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity. Discovered four decades ago in the context of card shuffling, this surprising phenomenon has since then been observed in a variety of models, from random walks on groups or complex networks to Glauber dynamics for high-temperature spin systems. It is now believed to be universal among fast-mixing high-dimensional processes. Yet, current proofs are heavily model-dependent, and identifying the general conditions that trigger a cutoff remains one of the biggest challenges in the quantitative analysis of finite Markov chains. In this talk, I will provide a self-contained introduction to this fascinating question, and then describe a recent partial answer based on entropy and curvature.

Monday 27th of October: Catherine Wolfram (ETH Zürich)

Epstein curves and holography of the Schwarzian action

Abstract: The circle can be seen as the boundary at infinity of the hyperbolic plane. We give a 1-to-2 dimensional holographic interpretation of the Schwarzian action, by showing that the Schwarzian action (which is a function of a diffeomorphism of the circle) is equal to the hyperbolic area enclosed by an "Epstein curve" in the disk. A dimension higher, the Epstein construction was used to relate the Loewner energy (a function of a Jordan curve related to SLE and Brownian loop measures) to renormalized volume in hyperbolic 3-space.

In this talk I will explain how to construct the Epstein curve, how the bi-local observables of Schwarzian field theory can be interpreted as a renormalized hyperbolic length using the same Epstein construction, and discuss what we know so far about the relationship between the Schwarzian action and the Loewner energy. This is based on joint work with Franco Vargas Pallete and Yilin Wang.

Monday 20th of October: Aleksei Kulikov (University of Copenhagen)

Time-frequency localization operator and its eigenvalues

Abstract: For a set A ⊂ R^d we denote by P_A the projection onto A and by Q_A = F⁻¹P_A F the Fourier projection onto A, where F is the Fourier transform. For a pair of sets A, B ⊂ R^d the time-frequency localization operator associated with A and B is the operator S_{A,B} = P_A Q_B P_A.

This is a self-adjoint operator satisfying 0 ≤ S_{A,B} ≤ Id. If A and B have finite measures then S_{A,B} is a Hilbert–Schmidt operator, in particular it is compact and so we have a sequence of eigenvalues 1 > λ₁(A, B) ≥ λ₂(A, B) ≥ ... ≥ 0.

If A = cA₁, B = cB₁ for some fixed nice sets A₁, B₁ and a big parameter c then the eigenvalues exhibit a phase transition: first ≈ c²ᵈ|A₁||B₁| of the eigenvalues are very close to 1, then there are only ≈ c²ᵈ⁻¹ log(c) intermediate eigenvalues, and the remaining eigenvalues tend to 0 extremely fast. Moreover, for fixed ε > 0 if we consider the counting function N_{c,ε} = #{n : ε < λₙ(c) < 1 − ε} then the dependence on 1/c is logarithmic as well. In this talk we will discuss the uniformity of the estimates on N_{c,ε} when ε is small. For a wide range of parameters we show a uniform bound c²ᵈ⁻¹ log(c)/ log(1/ε). Moreover, it turns out that if ε is extremely small, for example if ε < c⁻ᵃ, then the log(c) term disappears and the estimate becomes even better than expected.

The talk is based on joint works with Fedor Nazarov and with Martin Dam Larsen.

Monday 13th of October: Andrey Pilipenko (UNIGE)

Analytic and stochastic description of Brownian motions on star-like graphs

Abstract: Let S be a star-like graph, which is a union of finite number of rays with a common vertex 0. We provide a complete description of all Feller processes on S that behave like a Brownian motion on each ray until hitting 0. These processes are described from both an analytical and a stochastic point of view. The description includes:

(a) the construction of Markov semigroup generators on S with Wenzell-Feller boundary conditions at 0, which describe a mixture of reflection, killing, time delay, and jump exit at 0 with possibly infinite intensity, as well as the calculation of the explicit form of the resolvent of the process;

(b) representation of the process as a measurable function of finite number of Wiener processes and subordinators.

Monday 06th of October: Amirali Hannani (UNIGE)

Localization and Poisson statistics for the Quantum Sun Model (aka Avalanche model, Quantum Grain Model)

Abstract: In this talk, I first give a general overview of the concept of MBL (many-body localization), and I introduce the so-called quantum sun model (aka avalanche model/quantum grain model). Then, I discuss the significance of this model in the MBL community, including why it was introduced and its implications for the stability of MBL. Afterward, I present our result, proof of the localization, and Poisson statistics for this model in a certain range of parameters. Finally, I give some rough ideas about the proof: we first prove the result for the "free model" (sum of free disordered spin z), then we show that the interacting model is sufficiently "similar" to the free model by controlling the ratio of "in-resonance" levels. This is a joint work with Wojciech De Roeck.

Monday 29th of September: Nikita Gladkov (UNIGE)

Exploration in Bernoulli percolation

Abstract: Consider Bernoulli percolation on a graph, where edges are kept open independently with some probability. By revealing edges one at a time, one can analyze the structure of connected clusters and establish correlation inequalities for connectivity events. I will present several of these inequalities and outline the exploration-based arguments behind them.

Monday 22nd of September: Nicolas Curien (Université Paris-Saclay)

The Scaling Limit of Planar Maps with Large Faces

Abstract: In this work, we establish a scaling-limit result for Boltzmann-distributed models of random maps whose face degrees lie in the domain of attraction of a stable law of index α. This solves a problem posed some fifteen years ago. We thereby enlarge the family of canonical random metrics that arise as scaling limits of these map models, the most famous member of which is the Brownian sphere. 

Unlike the latter, the limits we obtain exhibit topologies reminiscent of Sierpiński sets, which depend on the value of α: if α > 3/2, the topology is the universal Sierpiński carpet, whereas if α < 3/2, the limiting space contains cut points. 

Along the way, we analyze fine properties of the continuous process that codes the distances in these limit spaces, which are necessary both for proving the scaling-limit results and for identifying their topology.

A variant of the famous KPZ conjecture states that the random metric spaces constructed this way are conjectured to appear as the chemical distance metric on CLE embedded in LQG.

Joint work with G. Miermont and A. Riera.

Monday 15th of September: Serte Donderwinkel (University of Groningen)

Random tree encodings and snakes

Abstract: There are several functional encodings of random trees which are commonly used to prove (among other things) scaling limit results. We consider two of these, the height process and Lukasiewicz path, in the classical setting of a branching process tree with critical offspring distribution of finite variance, conditioned to have n vertices. These processes converge jointly in distribution after rescaling by √n to constant multiples of the same standard Brownian excursion, as n goes to infinity. Their difference (taken with the appropriate constants), however, is a nice example of a discrete snake whose displacements are deterministic given the vertex degrees; to quote Marckert, it may be thought of as a “measure of internal complexity of the tree”. We prove that this discrete snake converges on rescaling by n^{-1/4} to the Brownian snakedriven by a Brownian excursion. This is a consequence of our new theory for “globally centred” discrete snakes that improves earlier works of Marckert and Janson and enjoys further applications in, for example, random maps. 

This talk is based on joint work with Louigi Addario-Berry, Christina Goldschmidt and Rivka Mitchell (https://arxiv.org/abs/2505.21823 )

Tuesday 10th of June: Wei Wu (NYU Shanghai)

Two dimensional dimers beyond planarity

Abstract: We study the dimer model and the spatial random permutation, and prove that on two-dimension like graphs (not necessarily planar), both the correlation function and the loop connectivity probability decays to zero. Our analysis is by introducing a new (complex) spin representation for models belonging to this class, and by deriving a new proof of the Mermin-Wagner theorem which does not require the positivity of the Gibbs measure. Based on joint work with Lorenzo Taggi (Sapienza)

Monday 2nd of June: Peter Wildemann (UNIGE)

Schwarzian Field Theory for Probabilists

Abstract: What does Liouville field theory, the SYK random matrix model and JT quantum gravity have in common? If you’d ask a physicist in recent years, they would be quick to point out that the low-energy behaviour of all these models should be described by the Schwarzian field theory. In itself, the latter can be understood as a probability measure on a quotient of the group of circle-diffeomorphisms Diff(T)/PSL(2,R). We discuss a rigorous approach to construct the measure in terms of a non-linear transformation of Brownian bridges, following ideas by Belokurov—Shavgulidze. Furthermore, we present new results that uniquely characterise the measure in terms of an appropriate change-of-variables formula, which can be seen as an analogue of the Cameron—Martin theorem on the space of circle diffeomorphisms. As a byproduct, we also obtain a short proof for the calculation of the measure’s partition function (i.e. total mass), confirming a prediction by Stanford—Witten. This talk is based on joint work with Roland Bauerschmidt and Ilya Losev.

Monday 26th of May: Loren Coquille (Université de Grenoble Alpes)

Delocalisation of the long-range Gaussian chain

Abstract: I will speak about the localisation/delocalisation properties of the discrete Gaussian chain with long-range interactions, which was the object of several conjectures since the nineties.

In a first paper with van Enter, Le Ny and Ruszel, we cooked up a very short proof of the absence of shift-invariant Gibbs states at any temperature for any interaction decay power α>2, which shows delocalisation of the chain in a non-quantitative manner.

Later on, in a second paper with Dario and Le Ny, we obtained a quantitative version of this delocalisation.

Combined with the results of Kjaer-Hilhorst, Fröhlich-Zegarlinski and Garban, our estimates provide an (almost) complete picture for the localisation/delocalisation of the discrete Gaussian chain. The proofs are based on graph surgery techniques which have been recently developed by van Engelenburg-Lis and Aizenman-Harel-Peled-Shapiro to study the phase transitions of two dimensional integer-valued height functions (and of their dual spin systems). 

Monday 12th of May: Philip Easo (Caltech)

Locality of the critical point for percolation

Abstract: I will sketch why the critical point for percolation on an infinite transitive graph G only depends on the geometry of G on small scales (except in the degenerate case when G is one-dimensional). This is based on joint work with Hutchcroft (https://arxiv.org/abs/2310.10983) and was predicted by Schramm around 2008. Our techniques are inspired by a lot of previous progress on the problem, most significantly by recent work of Contreras, Martineau, and Tassion, who handled the case of graphs with polynomial growth in 2022. Our proof uses random walks and the geometry of nilpotent groups in the service of percolation arguments.

Monday 5th of May: Clément Cosco (Université Paris Dauphine)

The subcritical phase of 2d directed polymers

Abstract: Directed polymers in random environment model the behavior of a long, directed chain that spreads among an inhomogeneous environment. Dimension two turns out to be critical for the model, which then exhibits a phase transition found by renormalizing the temperature at a suitable rate (Caravenna-Sun-Zygouras 17’).  In this talk, I will focus on the high temperature regime and present works in collaboration with Anna Donadini and Francesca Cottini about an elementary proof of the central limit theorem for the partition function (CSZ17) and its extension to space-correlated noise. The proof relies on a decomposition that also plays a central role in a related work with Shuta Nakajima and Ofer Zeitouni, where we study extreme value statistics of the partition function in connection to branching random walks (with a decreasing variance profile). I will try to explain this link, as well as some results about high moments estimates that we require for the proof.

Monday 28th of April: Andrew Charles Kenneth Swan (EPFL)

A new hyperbolic sigma model

Abstract: Recently, Sabot and Tarr\`es introduced a new type of vertex reinforced jump process: the $\star$-VRJP. It is defined on a directed graph $G$, which is equipped with a special involution $\star: G \rightarrow G$ that sends each vertex $j$ to a conjugate vertex $j^\star$, and each edge $\langle ij \rangle$ to a reversed conjugate edge $\langle j^\star i^\star \rangle$. Much like the ordinary VRJP, the $\star$-VRJP is linearly reinforced according to the local time of the walker, but where the ordinary VRJP prefers to jump to where it has been, the $\star$-VRJP prefers to jump to the \emph{conjugate} of where it has been. 

Also much like the ordinary VRJP, the $\star$-VRJP possesses a variety of remarkable integral identities through its ``magic formula" and random Sch\"odinger representation. In the case of the VRJP, through its connection with the  hyperbolic sigma model, the existence of these identities is seen to be a consequence of supersymmetric localisation: this naturally raises the question if there exists a ``$\star$-sigma model" counterpart to the $\star$-VRJP to give a similar supersymmetric explanation. In this talk, I will introduce this new $\star$-hyperbolic sigma model, the $\mathbb{H}^{2n+1|4m}_\star$-model, which is, in a sense, a complexification of the ordinary $\mathbb{H}^{n|2m}$-model, and will present several new isomorphism theorems which connect it to the $\star$-VRJP. Joint work with Sabot and Tarr\`es.

Monday 14th of April: Sébastien Ott (EPFL)

Finite volume mixing properties of lattice spin models

Abstract: Mixing properties of lattice spin models are ways to formalize the notion of information propagation/spatial dependency in these random fields.

I will present a family of notions making precise mixing properties of finite volume lattice spin models, in particular describing how boundary conditions do (or do not) affect information propagation inside a system. I will spend most of the time presenting an overview of what is known and applications. Then, I will present recent work on some of the issues in dimension 2, and, if time permits, briefly discuss less standard motivations for extensions of these questions to larger classes of models than the one considered up to now.

Monday 7th of April: Lisa Hartung (Johannes Gutenberg University Mainz)

Gaussian free field on the tree subject to a hard wall constraint

Abstract: We consider the Gaussian free field on a binary tree (also known as branching random walk) under the constraint that the values at all leaves at generation n are non-negative.  We obtain a remarkably precise description of the conditional law and the conditional field. The conditioning leads to an upward shift of the whole field. We obtain sharp estimates on this upward shift (up to o(1) terms). We show that the properly rescaled maximum converges to a Gumbel distribution (without a random shift!), and the rescaled minimum is exponentially distributed. We use tools from DGFFs on general graphs and estimates on random walks that are weakly attracted to zero either through a pinning potential or a drift. The talk is based on joint work with M. Fels (Technion) and O. Louidor (Technion).

Monday 31st of March: Thomas Budzinski (ENS Lyon)

The longest increasing subsequence of random separable permutations

Abstract: Consider a binary tree $T$ (i.e. with vertex degrees $1$ or $3$) decorated with positive or negative signs on its internal nodes. We are interested in the size of the largest subtree of $T$ where no negative node has degree 3. When $T$ is uniform among binary trees with size $n$ and the signs are i.i.d. Bernoulli with parameter $p$, this also describes the length of the longest increasing subsequence in natural models of random separable permutations. We will see that this quantity behaves like $n^{\alpha(p)+o(1)}$, where $\alpha(p)$ solves the following nice equation:
\[ \frac{2^{1/\alpha}\sqrt{\pi}\,\Gamma(1-1/(2\alpha))}{\Gamma(1/2-1/(2\alpha))}=\frac{p-1}{p}. \]
Based on ongoing work with Arka Adhikari, Jacopo Borga, William da Silva and Delphin Sénizergues

Monday 24th of March: Kamil Khettabi (UNIGE)

Phase separation in the planar Ising model

Abstract: Consider the planar Ising model with - boundary condition and beta>beta_c, h=0. We will study large deviation properties of the magnetization. We will see that for some values of the magnetization, the system creates a bubble of "+" in order to realize the deviation, and that this shape can be determined as the solution of a variational problem.

This can also be seen as providing a description of typical configurations of the Ising lattice gas in the canonical ensemble (that is, with a fixed number of particles).

I'll describe, in an informal way, the strategy of the proof in the classical setting developed in the 1990s. I'll then briefly present current work in progress, which aims at incorporating the effect of a gravitational field.

Monday 17th of March: Nikolai Bobenko (UNIGE)

Dimers and M-Curves: Limit Shapes from Riemann Surfaces

Abstract: We present a general approach for the study of dimer model limit shape problems via variational and integrable systems techniques. In particular we deduce the limit shape of the Aztec diamond and the hexagon for quasi-periodic weights through purely variational techniques. Putting an M-curve at the center of the construction allows one to define weights and algebro-geometric structures describing the behavior of the corresponding dimer model. We extend the quasi-periodic setup of our previous work to include a diffeomorphism from the spectral data to the liquid region of the dimer. Our novel method of proof is purely variational and exploits a duality between the dimer height function and its dual magnetic tension minimizer and applies to dimers with gas regions. We apply this to the Aztec diamond and hexagon domains to obtain explicit expressions for the complex structure of the liquid region of the dimer as well as the height function and its dual. We compute the weights and the limit shapes numerically using the Schottky uniformization technique. Simulations and predicted results match completely.

Monday 3rd of March: Nathanael Berestycki (Universität Wien)

On the spectral geometry of Liouville quantum gravity

Abstract: In this talk we will discuss the spectral geometry of the Laplace-Beltrami operator associated to Liouville quantum gravity. In particular we will show that the eigenvalues a.s. obey a Weyl law. This result (joint work with Mo Dick Wong) comes from an analysis of the LQG heat trace, which homogenises despite overwhelming pointwise fluctuations.

I will also discuss some conjectures which suggest a connection to "quantum chaos", and report on some ongoing work with Alcalde and Klein on the heat trace expansion.

Monday 16th of December : Lucas Rey (Paris)

Trees, forests and Doob transform

Abstract: The study of spanning trees dates back at least to the matrix-tree theorem of Kirchoff (1847). This theorem gives a determinantal formula for the number of spanning trees of a given graph. The study of random spanning trees (RST) was pushed further, using tools such as the transfer current theorem, or the Wilson’s algorithm which  samples RST using random walks. Another important tool for planar graphs is the Temperley’s bijection between spanning trees and dimer covers of an associated graph. More recently, in dimension 2, the scaling limit was established by Werner, Schramm, Lawler (2004) and universality results were also proved.

Spanning forests generalize spanning trees, and some of the tools mentioned above (but not all !) also apply to forests.

In this talk, we will explain how to use the Doob transform (or h-transform) to transfer the tools from the trees to the forests. As an application, we will present a universality result for the near-critical scaling limit of the RST model in dimension 2. 

Monday 09th December: Alessandro Pizzo (University of Rome "Tor Vergata")

Recent results on the spectral gap stability of quantum lattice systems

Abstract:  I will consider families of quantum lattice systems that have attracted much interest amongst people studying topological phases of matter. Their Hamiltonians are perturbations, by interactions of short range, of a Hamiltonian consisting of strictly local terms and with a (strictly positive) energy gap above its ground-state energy. I will review the main ideas of a novel method based on local Lie-Schwinger conjugations of the Hamiltonians associated with connected subsets of the lattice. By this method fermions and bosons are treated on the same footing, and our technique does not face a large field problem, even though bosons are involved. If time permits I will outline
a recent development concerning the control of the perturbation of a degenerate ground-state energy, which is the case of the AKLT Hamiltonian perturbed by small, finite-range potentials and with open boundary conditions imposed at the edges of the chain. (Joint works with S. Del Vecchio, J. Fröhlich, A. Ranallo, and S. Rossi.)

Monday 02nd of December: Lukas Lüchtrath (Berlin)

 Cluster sizes in subcritical soft Boolean models

Abstract: In this talk, we consider the soft Boolean model, a model that interpolates between two standard models of percolation: the classical Boolean model (viewed as a graph) and long-range percolation. Specifically, the model incorporates a heavy-tailed degree distribution and long-range edges. We study the subcritical one-arm probability and determine its tail behaviour. To this end, we explain how a path connecting the origin to a far distance relies on an interplay between the heavy-tailed degrees and the long-range edges. Furthermore, we compare the result with the tail probability of the number of vertices in a typical cluster, which depends on the degree-distribution alone. The proofs rest on a fine path-counting method, which we present in greater detail. The talk is based on joint work with Benedikt Jahnel and Marcel Ortgiese.

Monday 25th of November: Nicolas Forien (Paris) 

 Sandpiles, activated random walks and self-organized criticality 

Abstract: The abelian sandpile model is an elementary system of interacting particles which was suggested by physicists to illustrate the concept of self-organized criticality.

While the algebraic structure of this model enables its study through exact computations, its "constrained" nature leads to some of the predictions of physicists to turn out to be false.

This talk aims to present some recent developments and perspectives on activated random walks and stochastic sandpiles, which emerged as variants of the abelian sandpile model. These variants involve more randomness, and recent results indicate that they may correspond better to the physicists' original intuitions. 

Monday 18th of November: Bruno Schapira (Marseille)

 Intersection of high dimensional critical percolation clusters and Branching random walk ranges 

Abstract: Intersection of random walk ranges play a prominent role in different areas of probability theory and statistical physics. While this topic is now relatively well understood, at least for simple random walks on Euclidean lattices, much less is known for the intersection of critical branching random walks or critical percolation clusters. I will describe recent advances on this question. Joint (ongoing) work with Amine Asselah.

Monday 11th of November: Alessandro Giuliani (Rome)

 Electrical transport in 2D systems of interacting electrons: the Hall conductivity of the Haldane-Hubbard model

Abstract: Determining the effect of electron-electron interactions on transport coefficients is one of the central problems of solid state physics. While in many situations interactions are expected to affect the value of the conductivity, there are some special situations where transport coefficients appear to be "protected" (e.g., by symmetry or conservation laws) against interaction corrections. One important example is the Quantum Hall Effect, which concerns 2D electron systems subject to a transverse magnetic field. Evidence shows that at low temperatures the transverse conductivity is quantized in integer (or sometimes fractional) multiples of e^2/h, irrespective of disorder or interactions. In this talk I will consider a specific model of interacting electrons on the hexagonal lattice subject to a transverse dipolar magnetic field: the Haldane model with generalized Hubbard interactions. I will report rigorous results on the quantization of the transverse conductivity at weak enough interactions, in the whole "topological" phase diagram (i.e., for all values of the control parameters of the hopping Hamiltonian), including at the transition between the normal and Hall insulating phases. Based on joint works with V. Mastropietro, M. Porta, S. Fabbri, I. Jauslin, R. Reuvers. 

Monday 04th of November: Joscha Henheik (Rome)

 Zigzag strategy for random matrices

Abstract: It is a remarkable property of random matrices, that their resolvents tend to concentrate around a deterministic matrix as the dimension of the matrix tends to infinity, even for a small imaginary part of the involved spectral parameter.These estimates are called local laws and they are the cornerstone in most of the recent results in random matrix theory. In this talk, I will present a novel method of proving single-resolvent and multi-resolvent local laws for random matrices, the Zigzag strategy, which is a recursive tandem of the characteristic flow method and a Green function comparison argument. Novel results, which we obtained via the Zigzag strategy, include the optimal Eigenstate Thermalization Hypothesis (ETH) for Wigner matrices, uniformly in the spectrum, and universality of eigenvalue statistics at cusp singularities for correlated random matrices. Based on joint works with G. Cipolloni, L. Erdös, O. Kolupaiev, and V. Riabov. 

Monday 28st of October: Cristina Caraci (Geneva)

 The Ground State Energy of Dilute Bose Gases

Abstract: In this talk, I will present recent developments in the application of rigorous Bogoliubov theory to Bose gases confined to a 3D unit torus in the Gross-Pitaevskii regime. I will prove that the ground state energy can be determined with an error term that vanishes faster than (log N)/N, as N tends to infinity, with N number of particles. This result aligns with Wu's predictions from the 1950s in the physics literature. Based on joint work with Alessandro Olgiati, Diane Saint Aubin and Benjamin Schlein.

Monday 21st of October: Daniel Kious (Bath) 

 Sharp threshold for the ballisticity of the random walk on the exclusion process

Abstract:  In this talk, I will overview works on random walks in dynamical random environments. I will recall a result obtained in collaboration with Hilario and Teixeira and then I will focus on a work with Conchon--Kerjan and Rodriguez. Our main interest is to investigate the long-term behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, with density in [0,1]. At each jump, the random walker is subject to a drift that depends on whether it is sitting on top of a particle or a hole. We prove that the speed of the walk, seen as a function of the density, exists for all density but at most one, and that it is strictly monotonic. We will explain how this can be seen as a sharpness result and provide an outline of the proof, whose general strategy is inspired by techniques developed for studying the sharpness of strongly-correlated percolation models.

Monday 14th of October: Yacine Aoun (Geneva)

 Different flavours of the φ(S)-argument

Abstract:  I will explain a method that was developed by Duminil-Copin and Tassion to study the Bernoulli percolation model. After defining and explaining the original idea, we will see some new recent applications. 

Monday 7th of October: Titus Lupu (Sorbonne Université)

 Relation between the geometry of sign clusters of the 2D GFF and its Wick powers

Abstract: In 1990, Le Gall showed an asymptotic expansion of the epsilon-neighborhood of a planar Brownian trajectory (Wiener sausage) into powers of 1/|log eps|, that involves the renormalized self-intersection local times. In my talk I will present an analogue of this in the case of the 2D GFF. In the latter case, there is an asymptotic expansion of the epsilon-neighborhood of a sign cluster of the 2D GFF into half-integer powers of 1/|log eps|, with the coefficients of the expansion being related to the renormalized (Wick) powers of the GFF.

Monday 30th of September: Trishen Gunaratnam (Geneva)

 Adieu to phi^4_3

Abstract: The phi^4_3 model is one of the few 3d quantum field theories that mathematicians can rigorously analyze. There has been a huge amount of interest in the model since it was first constructed in the late '60s and, in my opinion, most of the relevant open problems about the model have been solved. There are, however, two quite pretty ones that persist. The first concerns establishing Segal axioms and the Markov property for phi^4_3. The second concerns establishing that phi^4_3 is the scaling limit of certain near-critical 3d Kac-Ising models. In this talk I will describe joint work with Nikolay Barashkov (Max Planck Leipzig) where we solve problem 1. Time and sense of reality distortion permitting, I will also touch upon some small but promising steps towards problem 2. That's based on ongoing work with Nikolay Barashkov, Simon Gabriel (Münster), and Markus Tempelmayr (Münster). Both approaches are based on a variational version of Polchinski's continuous renormalization group.

Monday 23rd of September: Hong-Quan Tran (Geneva) 

 Information percolation and mixing times of the Glauber-Exclusion process

Abstract: The Glauber-Exclusion process, an interacting particle system introduced by De Masi, Ferrari, and Lebowitz, is a superposition of a Glauber dynamics and the symmetric simple exclusion process (SSEP) on a lattice. It was shown to admit a reaction-diffusion equation as the hydrodynamic limit. In this talk, we introduce the information percolation framework invented by Lubetzky and Sly and explain how it can be used to study the mixing times of our process. After defining a notion of temperature regimes via the equation in the hydrodynamic limit, we prove cutoff for the attractive model in the high-temperature regime, analogous to the results of Lubetzky and Sly for the Glauber dynamics of the Ising model. Our results show a connection between the hydrodynamic limit and the mixing behavior of the large but finite system. 

Monday, 19th of June: Nicolas Curien (Orsay)

 Ideal Poisson-Voronoi tiling 

We study the limit in low intensity of Poisson--Voronoi tessellations in hyperbolic spaces. In contrast to the Euclidean setting, a limiting non-trivial ideal tessellation appears as the intensity tends to 0. The tessellation obtained is a natural Möbius-invariant decomposition of the hyperbolic space into countably many infinite convex polytopes, each with a unique end.  We study its basic properties, in particular the geometric features of its cells.
Based on joint works with Matteo d'Achille, Nathanael Enriquez, Russell Lyons and Meltem Unel.

Monday, 12th of June: Nathanael Berestycki (Vienna)

 Near-critical dimers and massive SLE

A programme initiated by Makarov and Smirnov is to describe near-critical scaling limits of planar statistical mechanics models in terms of massive SLE and/or Gaussian free field. We consider here the dimer model on the square or hexagonal lattice with doubly periodic weights, which is known to have non Gaussian limits in the whole plane. In joint work with Levi Haunschmid (TU Vienna) we obtain the following results: (a) we establish a rigourous connection with the massive SLE$_2$ constructed by Makarov and Smirnov; (b) we show that the convergence of the height function in arbitrary bounded domains subject to Temperleyan boundary conditions, and that the scaling limit is universal; and (c) we prove conformal covariance of the scaling limit. Our techniques rely on Temperley's bijection and the "imaginary geometry" approach developed in earlier work with Benoit Laslier and Gourab Ray, as well as a new exact discrete Girsanov identity on the triangular lattice. Time-permitting we will discuss conjectures relating this model to the sine-Gordon model. 

Tuesday, 30th of May: Eveliina Peltola (Aalto & Bonn)

On large deviations of SLEs, real rational functions, and zeta-regularized determinants of Laplacians

When studying large deviations (LDP) of Schramm-Loewner evolution (SLE) curves, a ''Loewner energy", and "Loewner potential'', that describe the rate function for the LDP, were recently introduced. While these objects were originally derived from SLE theory, they turned out to have several intrinsic, and perhaps surprising, connections to various fields. I will discuss some of these connections and interpretations towards Brownian loops, semiclassical limits of certain correlation functions in conformal field theory, and rational functions with real critical points (Shapiro-Shapiro conjecture in real enumerative geometry).

Based on joint work with Yilin Wang (IHES).

Monday, 22th of May: Amanda Turner (Leeds)

A statistical mechanics approach to planar aggregation

Planar random growth processes occur widely in the physical world. Examples include diffusion-limited aggregation (DLA) for mineral deposition and the Eden model for biological cell growth. One approach to mathematically modelling such processes is to represent the randomly growing clusters as compositions of conformal mappings. The Aggregate Loewner Evolution (ALE) model, formulated in this way,  provides a means of interpolating between the Eden model and DLA through varying a single parameter. An intriguing property is a conjectured phase transition between models that converge to growing disks, and 'turbulent' non-disk like models, but as yet there is no satisfactory explanation for this phenomenon. In this talk I will show how ALE can be formulated as a statistical mechanics model which provides a possible framework in which to explore the existence of phase transitions.

Monday, 15th of May: Ajay Chandra (Imperial College) & Ilya Chevyrev (Edinburgh)

Loop expansions for lattice gauge theories

In this two-part talk, we will present a loop expansion for lattice gauge theories and show how it applies to show ultraviolet stability in the Abelian Higgs model. In the first part, we will describe the loop expansion and related works of Brydges-Frohlich-Seiler. In the second part, we will show how the expansion can be applied to obtain a quantitative diamagnetic inequality. Combined with suitable lattice gauge fixing, the diamagnetic inequality allows us to show moment bounds on the gauge field marginal, uniform in the lattice spacing, when measured in Holder-Besov-type spaces. 

Monday, 8th of May: Alain Joye (Grenoble)

Mathematical (De-)Localisation for the Chalker-Coddington Model

The Chalker-Coddington model is a simplified, discrete version of the quantum dynamics of an electron in the plane submitted to a random potential and strong magnetic field. After a description of its construction and main properties, we shall review some mathematical results regarding the localisation and transport properties of the Chalker-Coddington model in various setups.

Tuesday, 2nd of May: Scott Armstrong (NYU)

Quantitative homogenization in high contrast

Consider the random conductance model on the Zd lattice where the conductivity function is iid and bounded between two positive constants. There has been a lot of work in recent years in developing very fine quantitative estimates for the behavior of harmonic functions (or equivalently, random walks) on large scales. These estimates are sharp in the limit of asymptotic scale separation. They however depend very badly on the "ellipticity contrast," that is, the ratio of largest to smallest possible value of the conductivities. It is an open problem to develop non-ridiculous estimates for the length scale at which homogenization begins to be seen, as a function of the ellipticity contrast. I will present a first result in this direction, and compare it to some estimates in percolation theory. (Joint work with Tuomo Kuusi.)

Tuesday, 2nd of May: Sylvia Serfaty (NYU)

Recent developments on Coulomb gases

  We will present a review on results on the Coulomb gas in general dimension: local laws describing the system down to micro scale, LDP for empirical field, CLT for fluctuations and hyper uniformity in dimension 2.

Monday, 24th of March: Steffen Polzer (Unige)

Renewal approach for the energy-momentum relation of the Polaron

The Fröhlich polaron is a model for the interaction of an electron with a polar crystal. We study the energy-momentum relation E(P) which is the bottom of the spectrum of the fixed total momentum Hamiltonian H(P). An application of the Feynman-Kac formula leads to Brownian motion perturbed by a pair potential. The point process representation introduced by Mukherjee and Varadhan represents this path measure as a mixture of Gaussian measures, the respective mixing measure can be interpreted in terms of a perturbed birth and death process. We apply the renewal structure of this point process representation in order to obtain a representation of a diagonal element of the resolvent of H(P). This then yields several properties of the energy-momentum relation, such as monotonicity in |P| and that the correction to the quasi-particle energy is negative.

Monday, 17th of April: Franco Severo (ETHZ)

On the size of level-set components for strongly correlated Gaussian fields

We study the level-sets of smooth Gaussian fields on R^d with slow decay of correlations (i.e. algebraic decay with exponent smaller than 1). As the level varies, this defines a percolation model, for which we compute the exact exponential rate of decay in probability for the size of subcritical connected components. This rate turns out to be proportional to the inverse correlation times the square of the distance to the critical level. This differs drastically from fields with fast decay of correlations, for which the cluster size probability always decays exponentially, and the precise rate constant is not well understood. Our result is an evidence in support of physicists' predictions for the characteristic length exponent of fields with slow algebraic decay of correlations, and also opens to way to the study of other large deviations questions for smooth Gaussian fields. In this talk, I aim at explaining how the existence of strong correlations leads to a (perhaps surprisingly) better understanding of these large deviation questions. This is based on a joint work with Stephen Muirhead.

Monday, 3rd of April: Martin Hairer (EPFL)

Renormalisation & Symmetries

Monday, 27th of March: Tyler Helmuth (Durham)

The Arboreal Gas

In Bernoulli bond percolation each edge of a graph is declared open with probability p, and closed otherwise. Typically one asks questions about the geometry of the random subgraph of open edges. The arboreal gas is the probability measure obtained by conditioning on the event that the percolation subgraph is a forest, i.e., contains no cycles. Physically, this is a model for studying the gelation of branched polymers. Mathematically it is the q->0 limit of the random cluster model. What are the percolative properties of these random forests? Do they contain giant trees? I will discuss what is known, what is conjectured, and how a connection with spin systems allows for analysis and intuition.

Monday, 20th of March: Nikolay Barashkov (Helsinki)

The $\phi^4_3$ model and towards Segal's axioms

The $\phi^4_3$ model is a 3-dimensional non-Gaussian Euclidean QFT. Showing existence of such a measure was one of the highlights of the constructive QFT programme in the '70s. In this talk I will describe joint work with Trishen Gunaratnam in analysing how different $\phi^4_3$ models glue together on cylinders.

Monday, 13th of March: Pierre Germain (Imperial)

Weak turbulence and the wave kinetic equation

The wave kinetic equation is expected to provide a description of weak turbulence, which is the chaotic dynamics appearing in weakly nonlinear systems. This (deterministic) kinetic equation should describe energy transfer between scales, and provides an entrypoint into the (random) world of turbulence. I will present these ideas and recent progress in this area.

Monday, 6th of March: Paul Dario (CNRS, UPEC)
Localization and delocalization for a class of degenerate convex grad phi interface model

In this talk, we will consider a classical model of random interfaces known as the grad phi (or Ginzburg-Landau) model. The model first received rigorous consideration in the work of Brascamp-Lieb-Lebowitz in 1975. Since then, it has been extensively studied by the mathematical community and various aspects of the model have been investigated regarding for instance the localization and delocalization of the interface, the hydrodynamical limit, the scaling limit, large deviations etc.  Most of these results were originally established under the assumption that the potential encoding the definition of the model is uniformly convex, and it has been an active line of research to extend these results beyond the assumption of uniform convexity. In this talk, we will introduce the model, some of its main properties, and discuss a result of localization and delocalization for a class of convex (but not uniformly convex) potentials.

Monday, 27th of February: Sungchul Park (KIAS)

Analysis of the planar Ising model under massive scaling limit

We give an overview of recent convergence results for the Ising model in two dimensions under a massive scaling limit, including convergence of spin and energy correlations and martingale observables for its interfaces. In particular, we highlight the analytical ideas used to deal with different boundary conditions and directions of perturbation, in the presence of possibly rough boundary segments. Based on joint works with Chelkak, Wan, and others.

Monday, 06th of February: Ariel Perez Mellor (UNIGE)

Using Graph Theory to Unravel Born Oppenheimer Molecular Dynamics and Replica-Exchange Monte Carlo Simulation 

In this seminar, I intend to introduce to you how graph theory analysis can be applied in the field of theoretical chemistry. I will discuss the treatment of a set Born-Oppenheimer molecular dynamics and a replica-exchange Monte Carlo trajectories. The first part of the talk will be dedicated to laying the foundations of the methodology by defining the necessary mathematical objects [1]. It includes the definition of colored graphs and their representation through the adjacency matrix together with the introduction of some properties that they must fulfil. At this point, I will discuss the isomorphism problem that arises when two identical atoms are swapped and how it can be solved. The second part will be devoted to the applications of the methodology. I will bring your attention to understanding the complex gas phase dissociation dynamics of three systems: the protonated cyclo Gly-Gly and the naphthalene and azulene cations. Finally, I will explain how the methodology can be extended to the analysis of a set of replica-exchange Monte-Carlo trajectories. 

Tuesday, 20th of December: Benoit Collins (Kyoto University)

New results around the norm of random matrices and operator-valued non-backtracking theory 

Non-backtracking operators have long ago proved to be very useful in (random) graph theory, e.g., in the study of (almost) Ramanujan graphs. A couple of years ago, we noticed that this theory extends in various directions: (1) uniformly equal coefficients of the operator can be replaced by matrix-valued coefficients to handle much more general adjacency matrices (thanks to a linearization trick), (2) the very generators of the non-backtracking operators, that were initially permutations, can be replaced by arbitrary unitary operators. We will report on recent progress along these lines, with new applications to random matrix theory and operator algebra. Time allowing I will also elaborate on the theory of “linearization tricks”, including new results for unitary operators. This work is based on past and ongoing work with Charles Bordenave.

Monday, 12th of December: Piet Lammers (IHES)

Planarity, percolation, and height functions

Fröhlich and Spencer proved the Berezinskii-Kosterlitz-Thouless transition in 1981, through a relation with delocalisation of height functions. My talk focuses on the phase transition for height functions. We mix ideas coming from height functions and planar percolation models in order to prove a coarse-graining inequality inspired by the renormalisation group picture. This allows us to make precise statements about the phase transition (e.g. sharpness) even without knowing exactly where this transition point lies. This talk is based on the recent preprint arXiv:2211.14365. 

Monday, 5th of December: Sébastien Martineau (UPMC)

Percolation on homogeneous graphs of polynomial growth 

Bernoulli percolation consists in erasing independently each edge of a graph G with some probability 1-p and studying the connected components (called clusters) of this random graph. Of interest is the parameter pc(G) above which infinite clusters exist. In this talk, we focus on homogeneous (= transitive) graphs for which the cardinality of balls is upper-bounded by a polynomial function of the radius. For such graphs, we get a good understanding of the supercritical regime p>pc (supercritical sharpness). From this, we deduce that Schramm's locality conjecture holds for such graphs: if you give me a ball of radius 10^10 of such a graph G, it is in principle possible for me to tell you "either pc(G)=1 or pc(G) is very close to [some specific value depending on the ball]". This is joint work with Daniel Contreras and Vincent Tassion.

Monday, 28th of November: Giuseppe Cannizzaro (Warwick)

Diffusion in the curl of the two-dimensional Gaussian Free Field 

I will discuss the large time behaviour of a Brownian diffusion in two dimensions, whose drift is divergence-free and ergodic, and given by the curl of the two-dimensional Gaussian Free Field. Together with L. Haundschmid and F. Toninelli, we prove the conjecture by B. Tóth and B. Valkó that the mean square displacement is of order $t \sqrt{\log t}$. The same type of superdiffusive behaviour has been predicted to occur for a wide variety of (self)-interacting diffusions in dimension d = 2, including the diffusion of a tracer particle in a fluid, self-repelling polymers and random walks, Brownian particles in divergence-free random environments, and, more recently, the 2-dimensional critical Anisotropic KPZ equation. To the best of our knowledge, ours is the first instance in which $\sqrt{\log t}$-superdiffusion is rigorously established in this universality class. 

Monday, 21st of November: Charles Bordenave (CNRS - Institut mathématique de Marseille) 

Mobility Edge of Lévy Matrices 

This is a joint work with Amol Aggarwal and Patrick Lopatto. Lévy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an α-stable law. For α<1, predictions from the physics literature suggest that high-dimensional Lévy matrices should display the following phase transition at a point Emob. Eigenvectors corresponding to eigenvalues in (−Emob,Emob) should be delocalized, while eigenvectors corresponding to eigenvalues outside of this interval should be localized. Further, Emob is given by the (presumably unique) positive solution to λ(E,α)=1, where λ is an explicit function of E and α.

We prove the following results about high-dimensional Lévy matrices.

(1) If λ(E,α)>1 then eigenvectors with eigenvalues near E are delocalized.

(2) If E is in the connected components of the set {x:λ(x,α)<1} containing ±∞, then eigenvectors with eigenvalues near E are localized.

(3) For α sufficiently near 0 or 1, there is a unique positive solution E=Emob to λ(E,α)=1, demonstrating the existence of a (unique) phase transition.

(a) If α is close to 0, then Emob scales approximately as |logα|^(−2/α).

(b) If α is close to 1, then Emob scales as (1−α)^(−1).

Our proofs proceed through an analysis of the local weak limit of a Lévy matrix, given by a certain infinite-dimensional, heavy-tailed operator on the Poisson weighted infinite tree. 

Monday, 14th of November: Dmitri Krachun (UNIGE)

Blume Capel model on Z^d

The Blume-Capel model can be seen as a natural generalisation of the Ising model, where spins are allowed to take value in $\{-1, 0, 1\}$. In this talk I will introduce the model and discuss its conjectural phase diagram as well as some classical and new connections to the Ising model. While presenting the main ideas of the proofs concerning the behaviour of the model on $\mathbb{Z}^d$, I will show how many beautiful probabilistic techniques developed over the last decades to study Ising and percolation models allow to rigorously study various regimes of the Blume-Capel model and its phase transition. Based on joint work with Trishen Gunaratnam and Christoforos Panagiotis 

Monday, 7th of November: Juhan Aru (EPFL)

A Green's function for CLE_4 and twist fields of the 2d GFF 

We will discuss how exploring and exploiting connections between CLE_4, GFF and loop soups can help rediscover old formulas appearing in  c = 1 conformal field theories related to the critical Ashkin-Teller model(s). This is joint work with F. Gabriel and T. Lupu. 

Monday, 17th of October 2022: Laurin Köhler-Schindler (ETHZ)

Scaling limits and arm exponents for the planar fuzzy Potts model

The fuzzy Potts model is obtained by independently coloring the clusters of a Fortuin-Kasteleyn (FK) percolation. We study the model on the square lattice when the FK percolation is critical. Under the assumption that this critical FK percolation converges to a conformally invariant scaling limit (which is known to hold for the FK-Ising model), we show that the obtained coloring converges to variants of Conformal Loop Ensembles constructed, described and studied by Miller, Sheffield and Werner. Using discrete considerations, we also show that the arm exponents for this coloring in the discrete model are identical to the ones of the continuum model. This allows us to determine the arm exponents for the planar fuzzy Potts model. Joint work with Matthis Lehmkuehler. 

Monday, 10th of October 2022: Barbara Dembin (ETHZ)

Almost sharp sharpness for Boolean percolation

We consider a Poisson point process on $\mathbb R ^d$ with intensity $\lambda$ for $d\ge2$. On each point, we independently center a ball whose radius is distributed according to some power-law distribution $\mu$. When the distribution $\mu$ has a finite $d$-moment, there exists a non-trivial phase transition in $\lambda$ associated to the existence of an infinite connected component of balls. We aim here to prove subcritical sharpness that is that the subcritical regime behaves well in some sense. For distribution $\mu$ with a finite $5d−3$-moment, Duminil-Copin--Raoufi--Tassion proved subcritical sharpness using randomized algorithm. We prove here using different methods that the subcritical regime is sharp for all but a countable number of power-law distributions.

Joint work with Vincent Tassion.  

Monday, 3rd of October 2022: Alexis Prévost (UNIGE)

Critical exponents for a percolation model on transient graphs

I will present some conjectures about critical exponents for percolation models with long-range correlations, and explain how these conjectures are solved in the specific case of level sets percolation for the Gaussian free field on the cable system. An essential role will be played by a certain capacity functional of the level sets, which appear naturally in a differential formula associated with this model. In particular, one can explicitly compute the law of the capacity of bounded clusters, and deduce asymptotics for various quantities in the critical or near-critical regime, such as the percolation probability or two points function. The talk is based on joint work with Alexander Drewitz and Pierre-François Rodriguez.  

Monday, 26th of September 2022: Benoit Dagallier (Cambridge)

Log-Sobolev inequality for the continuum phi^4_2 and phi^4_3 models

In this talk, I will report on a joint work with Roland Bauerschmidt in which we analyse the Langevin dynamics associated with the continuum phi4 model. The continuum phi4 model is one of the simplest models of field theory, introduced at least 50 years ago in the physics community. It can be thought of as a continuous analogue of the Ising model. In particular, it exhibits a phase transition, separating a weakly correlated and a strongly correlated regime. The presence of a phase transition should imply a dramatic difference in how much time it takes for the dynamics to approach its steady state, from fast convergence above the critical point, to slow convergence diverging with the system size below it. The analysis of the model is made particularly subtle due to the fact that the continuum limit is ill-defined, in the sense that a certain renormalisation procedure is needed to make sense of it. We characterise the relaxation to the steady state by proving a logarithmic Sobolev inequality (LSI) with constant bounded under optimal assumptions. The proof makes use of a very general LSI criterion developed in 2019 by Roland Bauerschmidt and Thierry Bodineau. 

In the talk, I will introduce the phi4 model and LSI inequalities, then try to explain the main ideas as non-technically as possible. 

Monday, 19th of September 2022: Aymeric Perriard (UNIGE)

Observation of the abelian sandpile model from numerical simulations

We will first present the Abelian sandpile model.  We will then look numerically at the behaviour of the one-dimensional model, and complexify it little by little to reach the two-dimensional rectangular lattice. For each graph, we observed the numerical distribution of avalanches and tried to understand why and how the distributions converge to a power law. Finally, we will look at the behaviour of the model and in particular the avalanche geometry for a particular graph "halfway" between the one and two dimensional graph. 

25/05/22. Yannick Couzinie

16/05/22. Lucas D'Alimonte and Romain Panis

02/05/22. John Haslegrave

25/04/22. Arnaud Le Ny

11/04/22. Pierre-François Rodriguez

04/04/22. Gady Kozma

28/03/22. Guillaume Baverez

21/03/22. Rémy Mahfouf

14/03/22. Nikolay Barashkov and Michael Hofstetter

07/03/22. Larissa Richards

26/01/22. Yonatan Gutman

13/12/21. Marcin Lis

29/11/21. Jian Ding and Jian Song

22/11/21. Christophe Garban

15/11/21. Maxime Savoy

08/11/21. Nikos Zygouras

01/11/21. Ewain Gwynne

25/10/21. Vittoria Silvestre

18/10/21. Daniel Sanchez

22/11/2021. Christophe Garban (ENS Lyon)

Continuous symmetry breaking along the Nishimori line

15/06/2020. Speaker: Yacine Aoun

Sharp asymptotics of correlation functions in the subcritical long-range random-cluster and Potts models 

25/05/2020. Speaker: Paul Melotti

The eight-vertex model via dimers

18/05/2020. Speaker: Antti Knowles

Field theory as a limit of interacting quantum Bose gases

11/05/2020. Speaker: Simone Warzel

Mean-Field Quantum Spin Glasses

04/05/2020. Speaker: Franco Severo

On the diameter of Gaussian free field excursion clusters away from criticality

27/04/2020. Speaker: Christophe Garban

Kosterlitz-Thouless transition and statistical reconstruction of the Gaussian free field

20/04/2020. Speaker: Thomas Leblanc

Two "physical" characterizations of the Sine-beta process

30/03/2020. Speaker: Hugo Duminil-Copin

Gaussianity of the 4D Ising model

09/03/2020. Speaker: Charles Bordenave

Strong asymptotic freeness for representations of independent Haar unitary matrices 

02/03/2020. Speaker: Raphaël Bucatez

Outliers for zeros of random polynomials and Coulomb gases

17/02/2020. Speaker: Marianna Russkikh

Dimers and embeddings

16/12/2019. Speaker: Lucas Benigni

Fermionic eigenvector moment flow 

02/12/2019. Speaker: Christopher J. Bishop

Weil-Petersson curves and finite total curvature.

02/12/2019. Speaker: Vieri Mastropietro

Renormalization Group approach to universality in non-integrable systems

25/11/2019. Speaker: Izabella Stuhl

The hard-core model in discrete 2D: ground states, dominance, Gibbs measures

18/11/2019. Speaker: Mikhail Khristoforov

Discrete multi-point and vector-valued observables in percolation.

12/11/2019. Speaker: Tyler Helmuth

Random spanning forests and hyperbolic symmetry

11/11/2019. Speaker: Nicolai Reshetikhin

Limit shapes in statistical mechanics

04/11/2019. Speaker: Christian Webb

How much can the eigenvalues of a random Hermitian matrix fluctuate?

28/10/2019. Speaker: Alessandro Olgiati

Stability of the Laughlin phase in presence of interactions

21/10/2019. Speaker: Daniel Lenz

Spectral theory of one-dimensional quasicrystals

14/10/2019. Speaker: Phan Thành Nam

Nonlinear Gibbs measures as the limit of equilibrium quantum Bose gases

07/10/2019. Speaker: Jonathan Hermon

Anchored expansion in supercritical percolation on nonamenable graphs

30/09/2019. Speaker: Vittoria Silvestri

Fluctuations and mixing of Internal DLA on cylinders

23/09/2019. Speaker: Dominik Schröder

Edge Universality for non-Hermitian Random Matrices

16/09/2019. Speaker: Antti Knowles

Expander graphs and the spectral gap of random regular graphs

27/05/2019. Speaker: Roland Bauerschmidt

Log-Sobolev inequalities for some strongly correlated spin systems

21/05/2019. Speaker: Tom Hutchcroft

Percolation critical exponents inequalities via randomised algorithms

13/05/2019. Speaker: Lukas Schoug

Dimensions of the two-valued sets of the 2D GFF

06/05/2019. Speaker: Eero Saksman

Decompositions of log-correlated fields with applications

29/04/2019. Speaker: Karen Habermann

A semicircle law and decorrelation for iterated Kolmogorov loops

15/04/2019. Speaker: Roman Boykiy

Dimensions of LQG-type random maps

08/04/2019. Speaker: Janne Junnila

Imaginary multiplicative chaos and the XOR-Ising model

01/04/2019. Speaker: Jean-Pierre Eckmann

Hamiltonian breathers with dissipation

25/03/2019. Speaker: Noam Berger

Moment estimates for regenerations in RWRE in the absence of a zero-one law

18/03/2019. Speaker: Ellen Powell

Welding critical LQG surfaces

11/03/2019. Speaker: Pierre Collet

Time scales in some large population birth and death processes, quasistationary distribution and resilience

04/03/2019. Speaker: Franck Gabriel

Neural Tangent Kernel: Convergence and Generalization in Neural Networks (joint work with Arthur Jacot and Clément Hongler)

25/02/2019. Speaker: Eveliina Peltola

Crossing probabilities of multiple Ising interfaces

17/12/2018. Speaker: Giovanni Antinucci

A Hierarchical Supersymmetric Model for Weakly Disordered 3d Semimetals 

10/12/2018. Speaker: Alain Joye

Representations of canonical commutation relations describing infinite coherent states

26/11/2018. Speaker: Mikhail Basok

Tau-functions a la Dubedat and cylindrical events in the double-dimer model

19/11/2018. Speaker: David Belius

The TAP-Plefka variational principle for mean field spin glasses

12/11/2018. Speaker: Damien Gayet

Percolation without FKG 

05/11/2018. Speaker: Benoit Laslier

Logarithmic variance for uniform homomorphisms on Z^2 

29/10/2018 and 30/10/2018.

SPECIAL EVENT: 4 x 45min lectures by Yilin Wang

Monday 29.10, 15:15-16:00 and 16:45-17:00, ACACIAS, SM17

Tuesday 30.10, 15:00-15:45 and 16:15-17:00, ACACIAS, SwissMap Meeting Room, 3rd floor

The Loewner energy at the crossroad of random geometry, geometric function theory, and Teichmueller theory

22/10/2018. Speaker: Jiri Cerny

The maximal particle of branching random walk in random environment

15/10/2018. Speaker: Raphael Ducatez

Anderson model and random products of matrices

08/10/2018. Speaker: Thomas Budzinski

Supercritical causal maps: geodesics and simple random walk

01/10/2018. Speaker: Hugo Vanneuville

Level set percolation for Gaussian fields

24/09/2018. Speaker: Alexander Glazman

Random Lipschitz functions and 6-vertex model via spin representations

19/02/2018. Speaker: Misha Khristoforov

Title: An order/disorder perturbation of percolation model. A highroad to Cardy's formula.

26/02/2018. Speaker: Gaultier Lambert

Title: Stein's method for normal approximation of linear statistics of beta-ensembles

Slides

05/03/2018. Speaker: Lorenz Hilfiker

Title: Solutions to Thermodynamic Bethe Ansatz equations and Y-systems

12/03/2018. Speaker: Sasha Sodin

Title: Non-Hermitian random Schroedinger operators

26/03/2018. Speaker: Alessandro Giuliani

Title: Plate-nematic phase in a 3D hard-core particle system

09/04/2018. Speaker: Thierry Bodineau

Title: Perturbative regimes for deterministic dynamics of a diluted gas of hard spheres

16/04/2018. Speaker: Yilin Wang

Title: The Loewner energy of a simply connected domain on the Riemann sphere

23/04/2018. Speaker: Pierre Youssef

Title: On the norm of Gaussian random matrices

07/05/2018. Speaker: Nathanael Berestycki

Title: Dimer model on surfaces

14/05/2018. Speaker: Konstantin Izyurov

Title: Scaling limits of critical Ising correlations: convergence, fusion rules, applications to SLE

28/05/2018. Speaker: Alex Karrila

Title: Boundary visits of loop-erased random walks

04/06/2018. Speaker: Marcin Lis

Title: The double random current nesting field

Slides 

25/09/2017. Speaker: Alexander Glazman

Title: Phase transition in the loop O(n) model

02/10/2017. Speaker: Sung Chul Park

Title: Ising Model: Local Spin Correlations and Conformal Invariance

09/10/2017. Speaker: Yvan Velenik

Title: Ornstein-Zernike theory of Ising and Potts models: a review of some applications

16/10/2017. Speaker: Joonas Turunen

Title: Critical Ising model on infinite random triangulation of the half plane

06/11/2017. Speaker: Alexey Bufetov

Title: Stochastic vertex models and symmetric functions

Slides

13/11/2017. Speaker: Christophe Pittet

Title: Convergence rates in von Neumann ergodic theorems for free groups

20/11/2017. Speaker: Hao Wu

Title: Hypergeometric SLE and Convergence of Critical Planar Ising Interfaces

Slides

27/11/2017. Speaker: Ananth Sridhar

Title: Limit Shapes in the Stochastic Six Vertex Model

04/12/2017. Speaker: Johannes Alt

Title: Local inhomogeneous circular law

Slides

11/12/2017. Speaker: Sanjay Ramassamy

Title: Miquel dynamics on circle patterns

Slides

18/12/2017. Speaker: Daniel Ueltschi

Title: Random interchange model on the complete graph and the Poisson-Dirichlet distribution 

26/06/2017. Speaker: Vaughan Jones

Title: On scale invariance states of quantum spin chains

12/06/2017. Speaker: Nicolas Rougerie

Title: Fractional quantum Hall effect and generalized Coulomb gases

29/05/2017. Speaker: Noemi Kurt

Title: Mathematical population genetics and the seed bank coalescent

22/05/2017. Speaker: Andrea Agazzi

Title: Large Deviations Theory for Chemical Reaction Networks

15/05/2017. Speaker: Victor Kleptsyn

Title: Furstenberg theorem with a parameter and Anderson localization in dimension one

08/05/2017. Speaker: Kalle Kytölä

Title: Conformal field theory on lattice: from discrete complex analysis to Virasoro algebra

24/04/2017. Speaker: Fredrik Viklund

Title: Loop-erased walks and natural parametrization

10/04/2017. Speaker: Kevin Schnelli

Title: Addition of random matrices

06/04/2017. Speaker: Marianna Russkikh

Title: Playing dominos in different domains

03/04/2017. Speaker: Francis Comets

Title: Cover time for the random walk and Brownian motion on the two-dimensional torus and random interlacement

27/03/2017. Speaker: Margherita Disertori

Title: Some results on history dependent stochastic processes

13/03/2017. Speaker: Giambattista Giacomin

Title: Disorder and depinning transitions: the lattice free field case

06/03/2017. Speaker: Vincent Vargas

Title: An Introduction to Liouville Conformal Field Theory

27/02/2017. Speaker: Ellen Powell

Title: Critical branching diffusions in bounded domains

23/02/2017. Speaker: Yuri Kifer

Title: Some Extensions Of The Erdos-Renyi Law Of Large Numbers

20/02/2017. Speaker: Vadim Gorin

Title: Universal local limits for lozenge tilings and noncolliding random walks 

19/12/2016. Speaker: Felix Gunther

Title: Discrete complex analysis and discrete Riemann surfaces

12/12/2016. Speaker: Igor Krasovsky

Title: Splitting of a gap in the bulk of the spectrum of random matrices

05/12/2016. Speaker: Juhan Aru (ETHZ)

Title: Bounded-type local sets for the 2D Gaussian free field

28/11/2016. Speaker: Adrien Kassel

Title: A geometrical take on isomorphism theorems for random walks

21/11/2016. Speaker: Ismael Bailleul

Title: Singular PDEs

14/11/2016. Speaker: Matteo Marcozzi

Title: Non-Gaussian Wick polynomials and cumulants in kinetic theory

07/11/2016. Speaker: Antti Knowles

Title: Local laws as a gateway to the eigenvalue and eigenvector statistics of random matrices

31/10/2016. Speaker: Jakob Bjornberg

Title: Probabilistic methods for quantum spin systems

24/10/2016. Speaker: Vincent Beffara

Title: Percolation of random nodal lines

17/10/2016. Speaker: Wei Qian. (ETHZ)

Title: Decomposition of Brownian loop-soup clusters

10/10/2016. Speaker: Fabio Toninelli

Title: A class of (2+1)-dimensional growth process with explicit stationary measure

03/10/2016. Speaker: Jean-Christophe Mourrat

Title: Heat kernel upper bounds for interacting particle systems

26/09/2016. Speaker: Titus Lupu

Title: What the cable graph techniques can tell about the continuum Gaussian Free Field in dimension 2

19/09/2016. Speaker: Eveliina Peltola

Title: On correlation functions, scaling limits, and Schramm-Loewner evolutions 

Lundi 18 avril 2016: Sébastien Martineau (Weizmann Institute)

Lundi 11 avril 2016: Antal Jarai

Lundi 21 mars 2016: Gourab Ray (University of Cambridge) Universality for fluctuation in the dimer model.

Lundi 14 mars 2016: Tobias Müller (Utrecht University) The critical probability for confetti percolation equals 1/2 

Lundi 07 mars 2016: Alessandra Caraceni (Paris Sud) A stroll around Random Infinite Quadrangulations of the Plane 

Lundi 29 Février 2016: Camille Male (Paris 5) A free probability theory for permutation invariant random graphs and matrices 

Lundi 07 décembre: conférence in CIB

Lundi 30 novembre 2015: Nicolas Orantin (EPFL) Solving loop models on random lattices.

Lundi 23 novembre 2015: Benjamin Schlein (university of Zurich) Hartree-Fock dynamics for weakly interacting fermions

Lundi 16 novembre 2015: journée Lyon-Genève-Grenoble 

Lundi 09 novembre 2015: Nikolaos Zygouras (Warwick) Scaling limits of disordered systems: disorder relevance and universality.

Lundi 02 novembre 2015: Piotr Milos (Warsaw) Delocalization of two-dimensional random surfaces with hard-core constraints 

Lundi 26 octobre 2015: Noé Cuneo (Unige) Non-equilibrium steady states for chains of rotors

Lundi 19 octobre 2015: Daniel Ahlberg (IMPA) Scaling limits for the threshold window: When does a monotone Boolean function flip its outcome?

Lundi 12 octobre 2015: Vadim Kaloshin (University of Maryland) Stochastic Arnold diffusion of deterministic systems

Lundi 05 octobre 2015: conférence CIB

Lundi 28 septembre 2015: Dmitry Chelkak and David Cimasoni (Unige) On the combinatorics of the 2D Ising model

Lundi 21 septembre (talk in english) 2015: Viviane Baladi (ENS) Mélange exponentiel des flots billards de Sinai 

Mardi 15 septembre 2015: Dmitry Ioffe (technion) Effective model of facets formation and ordered walks under area tilts

Vendredi 11 septembre 2015: Michael Aizenman (Princeton) Ising model from the Random Current prospective

Lundi 24 aout 2015: Alexander Fribergh (university of Montreal) The ant in “a" labyrinth

06/07/2015. Speaker: Augusto Teixeira

Title: Percolation and local isoperimetric inequalities

15/04/2015. Speaker: Gabor Pete

Title: Noise sensitivity questions in percolation-like processes

16/03/2015. Speaker: Neal Madras

Title: Random Pattern-Avoiding Permutations

02/03/2015. Speaker: Bruno Benedetti

Title: Discrete Morse theory and the number of triangulated manifolds

23/02/2015. Speaker: Mikhail Shkolnikov

Title: Tropical curves from sandpiles 

15/12/2014. Speaker: Pierre-Louis Giscard

Title: Compactness and large deviations

08/12/2014. Speaker: Nicolas Rougerie

Classical Coulomb gases: mean-field approximation and beyond

24/11/2014. Speaker: Fabio Toninelli

Title: Entropic repulsion, metastability and large deviations for SOS interfaces

17/11/2014. Speaker: Antti Knowles

Title: Anisotropic local laws for random matrices

12/11/2014. Speaker: Patrik Ferrari

Title: Free energy fluctuations for directed polymers in 1+1 dimension

03/11/2014. Speaker: Alessandro Giuliani

Title: Height fluctuations in interacting dimers

27/10/2014. Speaker: Benoit Laslier

Title: Dynamique stochastique d'interface discrète et modèles de dimères

20/10/2014. Speaker:  Esa Järvenpää 

Title: Dimensions of random covering sets in Riemann manifolds

22/09/2014. Speaker: Yinon Spinka

Title: Phase structure of the loop O(n) model for large n

15/09/2014. Speaker: Pierre-Louis Giscard

Title: Of Walks and Graphs 

10/06/2014. Speaker: Ariel Yadin

Title: A Converse of Kleiner's Theorem for Linear Groups

02/06/2014. Speaker: Felix Guenther

Title: Discrete complex analysis - the medial graph approach

26/05/2014. Speaker: Slava Rychkov

Title: Conformal symmetry of critical fluctuations in three dimensions

23/05/2014. Speaker: Robin Pemantle

Title: Hexahedron recurrence, determinants and double dimer configurations

15/05/2014. Speaker: Ivan Corwin

Title: Integrable probability: beyond the Gaussian universality class

12/05/2014. Speaker: Ivan Corwin

Title: Spectral theory of ASEP, XXZ and the q-Hahn Boson process

03/03/2014. Speaker: Mikhail Katsnelson

Title: TITLE

28/02/2014. Speaker: Matan Harel

Title: The Localization Phase Transition in Random Geometric Graphs with Too Many Edges 

16/12/2013. Speaker: Alexandre Boritchev (Unige)

Title: The randomly forced 1D Burgers equation: stationary measure and turbulence.

25/11/2013. Speaker: Igor Krichever

Title: Real normalized differentials and their applications

18/11/2013. Speaker: Mahel Afif Younan (Unige)

Title: topological glasses 04.11.2013: Séminaire Lyon-Genève (voir page web)

11/11/2013. Speaker: Yves Le Jan (Paris 11)

Title: Amas de boucles markoviennes

28/10/2013. Speaker: Noam Berger (Technische Université de Munich)

Title: Local limit theorem for ballistic random walk in random environments.

28/10/2013. Speaker: John Cardy (Oxford)

Title: Lattice Stress Tensor and Conformal Ward Identities

21/10/2013. Speaker: Jean Bertoin (university of Zurich)

Title: The cut-tree of large recursive trees.

14/10/2013. Speaker: Nicolas Curien (Paris 6)

Title: On the conformal structure of random triangulations

7/10/2013. Speaker: Yacine Ikhlef (LPTHE, Université Pierre et Marie Curie/CNRS)

Title: Discrete parafermions and quantum-group symmetries

30/9/2013. Speaker: Nick Beaton

Title: Solvable models of self-avoiding walks

23/9/2013. Speaker: Vincent Vargas (CEREMADE)

Title: Complex Gaussian multiplicative chaos

19/9/2013. Speaker: Nikolai Makarov

Title: Dynamics of the Schwarz reflection

16/9/2013. Speaker: Rémi Rhodes (CEREMADE)

Title: Gaussian multiplicative chaos at criticality

9/9/2013. Speaker: Martin Hairer (Warwick)

Title: Dynamics near criticality

29/8/2013. Speaker: Scott Sheffield (MIT)

Title: QLE 

16/5/2013. Speaker: Alexandre Pouget (UNIGE)

Title: Neural computation as probabilistic inference

13/5/2013. Speaker: Laure Dumaz (ENS ulm)

Title: Some properties of the "true self repelling motion"

7/5/2013. Speaker: Omer Angel (UBC)

Title: 1 dimensional DLA

25/3/2013. Speaker: Juan Rivera-Letelier (Pontificia Universidad Catolica de Chile)

Title: Low-temperature phase transitions in the quadratic family

18/3/2013. Speaker: Sacha Glazman (Université de Genève)

Title: Connective constant for a weighted self-avoiding walk on~Z

11/3/2013. Speaker: Gaetan Borot (Université de Genève)

Title: All order asymptotics of beta ensembles in the multi-cut regime

28/2/2013. Speaker: Yuri Kifer (Hebrew University)

Title: Poisson and compound Poisson approximations in conventional and nonconventional setups

20/2/2013. Speaker: Piotr Milos (Warsaw)

Title: Delocalisation of the two-dimensional Lipschitz model 

17/12/2012. Speaker: Thierry Levy (Paris UPMC)

Title: The master field on the plane

10/12/2012. Speaker: Anthony Mays (Melbourne)

Title: A geometrical triumvirate of (non-Hermitian) random matrices

29/11/2012. Speaker: Jason Miller (MIT)

Title: Reversibility of SLE for kappa in (4,8)

26/11/2012. Speaker: Laurent Tournier (Université Paris XIII)

Title: Directional transience of oriented-edge reinforced random walks on Z^d

22/11/2012. Speaker: Hao Wu (Orsay)

Title: Conformally Invariant Growing Mechanism in CLE_4 and Couplings between GFF and CLE_4

19/11/2012. Speaker: Alex Fribergh (Toulouse)

Title: On the monotonicity of the speed of biaised random walk on a Galton-Watson tree without leaves

13/11/2012. Speaker: Nathanael Berestycki (Cambridge)

Title: A new approach to the Brownian web

5/11/2012. Speaker: Yair Hartman (Weizmann Institute)

Title: Random walks on groups and recurrent subgroups

29/10/2012. Speaker: Pierre-François Rodriguez (ETH)

Title: On the level-set percolation for the Gaussian free field

15/10/2012. Speaker: Béatrice de Tillière (UPMC)

Title: Loops in the XOR Ising model

8/10/2012. Speaker: Christophe Sabot (Université Lyon 1)

Title: Edge reinforced random walks, Vertex reinforced jump process, and the SuSy hyperbolic sigma model.

1/10/2012. Speaker: Amandine Veber (Ecole Polytechnique)

Title: Evolution of the interface between types in a spatially extended population

24/9/2012. Speaker: Igor Kortchemski (Orsay)

Title: Random trees conditioned to be large

17/9/2012. Speaker: Gordon Slade (UBC)

Title: Growth constants for lattice trees and lattice animals in high dimensions 

30/5/2012. Speaker: Jeremie Bettinelli (Orsay)

Title: Scaling limit of arbitrary genus random maps

22/5/2012. Speaker: Alain-Sol Sznitman (ETH)

Title: On Gaussian free fields and random interlacements

14/5/2012. Speaker: Rémi Peyre (Nancy)

Title: McKean–Vlasov Metastability

7/5/2012. Speaker: Pietro Caputo (Roma Tre)

Title: On the spectrum of random Markov matrices

2/5/2012. Speaker: Serge Richard (Université de Lyon)

Title: Théorèmes d'indice en théorie de la diffusion

26/4/2012. Speaker: Remco van Der Hofstad (Eindhoven University of technology)

Title: The survival probability and r-point functions in high dimensions

25/4/2012. Speaker: Ron Peled (Tel Aviv University)

Title: Probabilistic existence of rigid combinatorial structures

23/4/2012. Speaker: Nicolas Curien (ENS Ulm)

Title: relation between the intersection property and reccurence

16/4/2012. Speaker: Emanuel Millman (Technion)

Title: Transference Principles for Log-Sobolev and Spectral-Gap Inequalities with Applications to Conservative Spin Systems

2/4/2012. Speaker: Pierre Nolin (ETH)

Title: A modified frozen percolation process on the binary tree and on the square lattice

19/3/2012. Speaker: Raphael Cerf (Orsay)

Title: Nucleation and growth for the Ising model in d dimensions at very low temperatures

12/3/2012. Speaker: Marc Wouts (Paris XIII)

Title: Glauber dynamics for the quantum Ising model on a tree

7/3/2012. Speaker: Cyrille Lucas (Paris X)

Title: Internal Diffusion Limited Aggregation, from the centered to the drifted case

21/2/2012. Speaker: Ross Pinsky (Technion)

Title: Probabilistic and Combinatorial Aspects of the Card-Cyclic to Random Insertion Shuffle

20/2/2012. Speaker: Martin Hairer (Warwick)

Title: Solving the KPZ equation 

6/12/2011. Speaker: Vladislav Vysotsky

Title: Persistence of integrated random walks

9/12/2011. Speaker: Laszlo Erdos (Munich)

Title: The local version of Wigner's semicircle law and Dyson's Brownian motion

12/12/2011. Speaker: Gady Kozma (Weizman institute)

Title: Harmonic maps on Cayley graphs

13/12/2011. Speaker: Vladas Sidoravicius (IMPA)

Title: Stability of the waiter

19/12/2011. Speaker: Konstantin Izyourov (Université de Genève)

Title: soutenance de thèse

20/12/2011. Speaker: Ilya Gruzberg (University of Chicago)

Title: Quantum Hall transitions and conformal restriction

5/12/2011. Speaker: Ioan Manulescu (Cambridge)

Title: Bond Percolation on Isoradial Graphs

28/11/2011. Speaker: Thierry Bodineau (ENS Paris)

Title: Transition de phases pour des dynamiques avec contraintes

22/11/2011. Speaker: Mireille Bousquet-Mélou (university Bordeaux 1)

Title: The Potts model on planar maps

16/11/2011. Speaker: Nicolas Monod (EPFL)

Title: Littlewood and large forests

14/11/2011. Speaker: Damien Simon (UPCM)

Title: Some recent algebraic and probabilistic results on the asymmetric exclusion process with reservoirs

11/11/2011. Speaker: Wendelin Werner (Orsay)

Title: Describing surface fluctuations

3/11/2011. Speaker: Michael Monastyrsky (ITEP and EPFL)

Title: Kramers-Wannier Duality, Old and New Results

31/10/2011. Speaker: Paul Fendley (University of Virginia)

Title: Discrete Holomorphicity from Topology

24/10/2011. Speaker: Adrien Joseph (ENS Cachan)

Title: The component sizes of a critical random graph

17/10/2011. Speaker: Fabio Martinelli (University Roma tre)

Title: Sharp mixing time bounds for sampling random surfaces

13/10/2011. Speaker: Gregory Falkovich (Weizman)

Title: Broken and emerging symmetries of the turbulent state

10/10/2011. Speaker: Jérémie Bouttier (Institut de Physique Théorique)

Title: Des boucles sur les cartes aléatoires 

4/4/2011. Speaker: Bertrand Eynard (DSM-CEA/Saclay)

Title: Exact results for statistical models on random lattices

11/2/2011. Speaker: Nicolas Curien (Ecole normale supérieure)

Title: A view from infinity of the uniform infinite planar quadrangulation

22/11/2010. Speaker: Kostantin Izyurov (Université de Genève)

Title: Holomorphic spinor observables in the Ising model

17/11/2010. Speaker: Vladas Sidoravicius (IMPA)

Title: Abundance of maximal paths

15/11/2010. Speaker: Sacha Friedli (Universidade Federal de Minas Gerais)

Title: Singularités essentielles des potentiels thermodynamiques

8/11/2010. Speaker: Hubert Lacoin (Universita di Roma tre)

Title: Polymères dirigées en milieu aléatoire: diffusivité ou localisation

25/10/2010. Speaker: David Cimasoni (Université de Genève)

Title: La formule de Kac-Ward généralisée

19/10/2010. Speaker: Jan De Gier (University of Melbourne)

Title: Exact finite size percolation operator between boundaries of a lattice strip

4/10/2010. Speaker: Hugo Duminil-Copin (UNIGE)

Title: Self-avoiding walks on the hexagonal lattice 

Mardi 6 juillet, 2010 : Mohammad Rajabpour (INFN, Turin)

Ashkin-Teller model on the iso-radial graphs

Lundi 14 juin, 2010 : Ilya Gruzberg (Chicago University)

Stochastic Loewner chains for DLA-like growth

Jeudi 10 juin, 2010, à 16h15, en salle 17 : Vladimir Mangazeev (ANU, Canberra)

Quantum geometry of 3D lattices

Mercredi 2 juin, 2010, à 13h15 en salle 623 : Eldad Bettelheim (Hebrew University of Jerusalem)

Tau functions and differential equations for the real time evolution of free fermions

Mercredi 19 mai, 2010, 13h15, salle 623 : Jason Miller (Stanford)

Universality for SLE(4)

Lundi 17 mai 2010: Nikolai Makarov (Caltech)

Radial explorer and its two conformally invariant theories

Vendredi 14 mai 2010, 13 h 25, salle 623 : Hugo Duminil-Copin (UNIGE)

Groupe de travail sur RSW

Lundi 10 mai 2010: Rinat Kashaev (UNIGE)

Informal seminar about the colored Jones polynomial

Vendredi 8 mai 2010: Yacine Ikhlef (UNIGE)

Groupe de travail sur le modèle O(n)

Lundi 19 avril 2010: Nicholas Varopoulos (Unige) 

Green's function on quasidisks

Lundi 12 avril 2010 : Ilia Binder (Toronto) 

Efficient computation of harmonic measure and boundary geometry

Mercredi 24 mars 2010 : B. Doyon (King's College London)

Calculus on infinite-dimensional manifolds, conformal field theory, and its probabilistic descriptions

Lundi 22 mars 2010 : N. Curien (ENS)

Recursive triangulations and fragmentation theory

Lundi 15 mars 2010 : P. Nolin (Courant Institute)

Monochromatic arm exponents for 2D percolation 

Mercredi 3 mars 2010 : G. Miermont (Université Paris-Sud)

Scaling limits of random planar maps with large faces

Jeudi 4 février 2010 : N. Th. Varopoulos

Random walks in complex domains

Lundi 14 décembre 2009 : Rémi Peyre (ENS Lyon)

Variables aléatoires partiellement indépendantes : une approche hilbertienne

Vendredi 11 décembre 2009, 13h30 : Anton Alekseev (UNIGE)

Séminaire informel sur WZW, KZ et SLE

Lundi 7 décembre 2009 : Bernard Nienhuis

Critical percolation and qKZ equations

Mercredi 18 novembre 2009 : Kari Astala (Helsinki)

Informal seminar on random weldings and quasiconformal maps 

Lundi 16 novembre 2009: Antti Kupiainen (Helsinki)

Random Weldings

Jeudi 12 novembre 2009, 16h15, salle 17 : Phillipe Di Francesco (CEA Saclay)

Integrable Combinatorics

Vendredis 27 novembre et 4 décembre 2009 : Dmitry Beliaev (UNIGE)

On a theorem of Tsirelson

Lundi 30 novembre 2009 : Alain-Sol Sznitman (ETHZ)

Disconnection of discrete cylinders and random interlacements

Mercredi 11 novembre 2009 : séminaire informel

29 septembre et 15 octobre 2009 : Thierry Lévy (UNIGE) 

Mesure et action de Yang-Mills en deux dimensions

(séminaire Groupes de Lie et espaces de modules)

Lundi 28 septembre 2009 : Christophe Garban (ENS Lyon)

Near-critical and dynamical percolation scaling limits

Lundi 21 septembre 2009 : Vincent Beffara (ENS Lyon)

Slow progress on the slow bond problem

Vendredi 5 juin 2009, 15h15 : Nikolai Makarov (Caltech)

Random normal matrices

Lundi 18 mai 2009 : Antti Kemppainen (Helsinki)

Describing scaling limits of random planar curves by SLEs

Lundi 28 avril 2009 : Jürgen Angst (Strasbourg)

Mouvement brownien dans le cadre de la théorie de la relativité

Lundi 6 avril 2009 : Nicolas Orantin (CERN)

Énumération de cartes et matrices aléatoires

Lundi 30 mars 2009 : Adam Timar (Bonn)

Equivariant colorings of random planar graphs

Mardi 24 mars 2009, 14h00, salle 17 : Christian Mercat (Montpellier)

Surfaces de Riemann discrètes et modèle d'Ising

Lundi 9 mars 2009 : Nicolas Monod (EPFL)

Littlewood and Large Forests

Vendredi 6 mars 2009, 15h, salle 17 : Bernard Sapoval (École polytechnique et ENS Cachan)

Physical problems related to gradient and extreme gradient percolation

Lundi 15 décembre 2008 : Béatrice de Tilière (UNINE)

Lundi 24 novembre 2008 : Sacha Friedli (Belo Horizonte)

Chaînes à longue portée et le mécanisme de Bramson-Kalikow

Lundi 17 novembre 2008 : Istvan Prause

Harmonic measure and quasiconformal mappings

Lundi 10 novembre 2008 : Yacine Ikhlef

Observables holomorphes sur réseau et modèles de boucles intégrables

Lundi 3 novembre 2008 : David Ridout (DESY theory group, Hamburg)

Critical Percolation as a CFT (with a view to SLE)

Jeudi 30 octobre 2008 (13h, salle 623) : Viviane Baladi (ENS Paris)

Espaces de Banach adaptés aux dynamiques hyperboliques avec singularités et aux billards

Lundi 20 octobre 2008 : Cédric Boutillier (Université Paris VI et UniNE)

Scaling limits for random skew plane partitions with a piecewise periodic back wall

Jeudi 16 octobre 2008 (13h, salle 623) : David Cimasoni (ETHZ)

The dimer model, discrete spin structures and discrete d-bar operators

Lundi 6 octobre 2008 : Olivier Bernardi (Université Paris-Sud)

Comptage des cartes coloriées

Lundi 29 septembre 2008 : Bertrand Eynard (SPhT, CEA - Saclay)

Plancherel measure on partitions, matrix models and Gromov-Witten theory

Lundi 22 septembre 2008 : Gregory Miermont (Université Paris-Sud et ENS Paris)

Propriétés géométriques des grandes cartes aléatoires