moi     Loren Coquille's webpage  

I moved to the Hausdorff Center für Mathematik at the University of Bonn, Germany.
See http://wt.iam.uni-bonn.de/coquille/home

Until August 2013 I was PhD student at the Mathematics department of the University of Geneva.
My main interests are somewhere in the intersection between physical mathematics and mathematical physics...

Research and publications


Two notes on the discrete Gaussian Free Field with disordered pinning on $\mathbb Z^d$, $d\geq 2$.

Joint work with P. Miłoś.
We study the discrete massless Gaussian Free Field on $\mathbb Z^d$, $d\geq2$, in the presence of a disordered square-well potential supported on a finite strip around zero. The disorder is introduced by reward/penalty interaction coefficients, which are given by i.i.d. random variables.
In the first note, we prove under minimal assumptions on the law of the environment, that the quenched free energy associated to this model exists in $\mathbb R^+$, is deterministic, and strictly smaller than the annealed free energy whenever the latter is strictly positive.
In the second note, we consider Bernoulli reward/penalty coefficients $b\cdot e_x+h$ with $e_x\sim \text{Bernoulli}_{1/2}(-1,+1)$ for all $x\in\mathbb Z^d$, and $b>0$, $h\in\mathbb R$. We prove that in the plane $(b,h)$, the quenched critical line (separating the phases of positive and zero free energy) lies strictly below the line $h=0$, showing in particular that there exists a non trivial region where the field is localized though repulsed on average by the environment.

A note on the discrete Gaussian Free Field with disordered pinning on $\mathbb Z^d$, $d\geq 2$. L. Coquille, P. Miłoś, March 2013.
Accepted for publication in Stoch. Proc. Appl.
DOI 10.1016/j.spa.2013.04.022
[Preprint]

A second note on the discrete Gaussian Free Field with disordered pinning on $\mathbb Z^d$, $d\geq 2$. L. Coquille, P. Miłoś, March 2013.
[Preprint]


On the Gibbs states of the non-critical Potts model on $\mathbb Z^2$.

Joint work with H. Duminil-Copin, D. Ioffe, and Y. Velenik.
We prove that all Gibbs states of the supercritical $q$-state nearest neighbour Potts model on $\mathbb Z^2$ are convex combinations of the $q$ pure phases; in particular, they are all translation invariant. To achieve this goal, we consider such models in large finite boxes with arbitrary boundary condition, and prove that the center of the box lies deeply inside a pure phase with high probability. Our estimate of the finite-volume error term is of essentially optimal order, which stems from the Brownian scaling of fluctuating interfaces. The results hold at any supercritical value of the inverse temperature $\beta>\beta_c(q)=\log(1+\sqrt{q})$.

On the Gibbs states of the non-critical Potts model on $\mathbb Z^2$.
L. Coquille, H. Duminil-Copin, D. Ioffe, Y. Velenik. May 2012.
Accepted for publication in Probab. Theory Relat. Fields.
DOI 10.1007/s00440-013-0486-z
[Preprint]


A finite-volume version of Aizenman-Higuchi theorem for the $2d$ Ising model.

Joint work with Y. Velenik.
In the late 1970s, in two celebrated papers, Aizenman and Higuchi independently established that all infinite-volume Gibbs measures of the two-dimensional ferromagnetic nearest-neighbor Ising model at inverse temperature $\beta \geq 0$ are of the form $\alpha \mu_\beta^+ +(1-\alpha)\mu_\beta^-$, where $\mu_\beta^+$ and $\mu_\beta^-$ are the two pure phases and $0 \leq \alpha \leq 1$. We present here a new approach to this result, with a number of advantages: (i) We obtain a finite-volume, quantitative analogue (implying the classical claim); (ii) the scheme of our proof seems more natural and provides a better picture of the underlying phenomenon; (iii) this new approach seems substantially more robust.

A finite-volume version of Aizenman-Higuchi theorem for the $2d$ Ising model.
L. Coquille, Y. Velenik. April 2010.
Probab. Theory Relat. Fields 153 25-44 (2012).
DOI: 10.1007/s00440-011-0339-6
[Preprint] [Poster] [Slides]


Formation



Here you can download some documents I wrote during my undergraduate studies :

[PDF] De la non-localité ou le problème EPR2. Theoretical tutorial (in french), under the supervision of C. Branciard, in N. Gisin's group, February 2009.
Preprint (Branciard, Gisin, Scarani).

[PDF] Etude de l’équivalence et de la synthèse entre mécanique matricielle de Heisenberg et mécanique ondulatoire de Schrödinger. Historical work (in french), written for the lecture of History and Philosophy of Quantum Mechanics, given by J. Lacki, October 2006.


Teaching experience


2012-2013
2011-2012
2010-2011
2009-2010
2006-2007

Talks



Long duration stays


Attendance at conferences



Popularization