### Publications

Research articles

[73] A characterization of strong percolation via disconnection. with S. Goswami, P.-F. Rodriguez, F. Severo, A. Teixeira,, preprint.

[72] Phase transition for the vacant set of random walk and random interlacements. with S. Goswami, P.-F. Rodriguez, F. Severo, A. Teixeira,, preprint.

[71] Finite range interlacements and couplings. with S. Goswami, P.-F. Rodriguez, F. Severo, A. Teixeira, preprint.

[70] Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules. with I. Hartarsky, preprint.

[69] Near critical scaling relations for planar Bernoulli percolation without differential inequalities. with I. Manolescu and V. Tassion, preprint.

[68] Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension $d\ge 3$. with A. Rivera, P.F. Rodriguez, and H. Vanneuville, preprint.

[67] Conformal invariance of double random currents I: identification of the limit with M. Lis and W. Qian, preprint.

[66] Conformal invariance of double random currents II: tightness and properties in the discrete with M. Lis and W. Qian, preprint.

[65] Rotational invariance in critical planar lattice models with K.K. Kozlowski, D. Krachun, I. Manolescu, and M. Oulamara, preprint.

[64] Delocalization of the height function of the six-vertex model with A. Karrila, I. Manolescu, and M. Oulamara, preprint.

[63] On the six-vertex model’s free energy with K.K. Kozlowski, D. Krachun, I. Manolescu, and T. Tikhonovskaia, preprint.

[62] Planar random-cluster model: scaling relations with I. Manolescu, preprint.

[61] Long-range order for critical Book-Ising and Book-percolation with C. Garban and V. Tassion, preprint.

[60] Long-range models in 1D revisited with C. Garban and V. Tassion, preprint.

[59] Logarithmic variance for the height function of square-ice with M. Harel, B. Laslier, A. Raoufi, G. Ray.

[58] Equality of critical parameters for percolation of Gaussian free field level-sets with S. Goswami, P.F. Rodriguez and F. Severo, Duke Mathematical Journal. (to appear).

[57] Existence of phase transition for percolation using the Gaussian Free Field with S. Goswami, A. Raoufi, F. Severo and A. Yadin,

[56] Upper bounds on the percolation correlation length with G.Kozma and V. Tassion,

[55] Universality of two-dimensional critical cellular automata with B. Bollobás, R. Morris and P. Smith

[54] Discontinuity of the phase transition for the planar random-cluster and Potts models with $q>4$ with M. Gagnebin, M. Harel, I. Manolescu and V. Tassion.

[53] Renormalization of crossing probabilities in the planar random-cluster model with V. Tassion.

[52] Planar random-cluster model: fractal properties of the critical phase with I. Manolescu and V. Tassion.

[51] Marginal triviality of the scaling limits of critical 4D Ising and $\varphi_4^4$ models with M. Aizenman.

[50] Macroscopic loops in the loop $O(n)$ model at Nienhuis' critical point with A. Glazman, R. Peled and Y. Spinka

[49] A note on Schramm's locality conjecture for random-cluster models with V. Tassion

[48] Subcritical phase of $d$-dimensional Poisson-Boolean percolation and its vacant set with A. Raoufi and V. Tassion

[47] On the number of maximal paths in directed last-passage percolation with H. Kesten, F. Nazarov, Y. Peres, V. Sidoravicius

[46] Bounding the number of self-avoiding walks: Hammersley-Welsh with polygon insertion with S. Ganguly, A. Hammond and I. Manolescu

[45] Dimerization and Néel order in different quantum spin chains through a shared loop representation with M. Aizenman and S. Warzel.

[44] Internal Diffusion-Limited aggregation with uniform starting points with I. Benjamini, G. Kozma and C. Lucas,

[43] Exponential decay of truncated correlations for the Ising model in any dimension for all but the critical temperature with S. Goswami and A. Raoufi,

[42] On the double random current nesting field with M. Lis,

[41] Exponential decay of connection probabilities for subcritical Voronoi percolation in $\mathbb R^d$ with A. Raoufi and V. Tassion, PTRF.

[40] Minimal growth harmonic functions on lamplighter groups with I. Benjamini, G. Kozma and A. Yadin, New York J Math.

[39] Emergent Planarity in two-dimensional Ising Models with finite-range Interactions with M. Aizenman, V. Tassion and S. Warzel, Inventiones.

[38] A new computation of the critical point for the planar random-cluster model with $q\ge1$ with A. Raoufi and V. Tassion, Ann. IHP.

[37] Higher order corrections for anisotropic bootstrap percolation with A. C. D. van Enter and T. Hulshof, PTRF .

[36] The box-crossing property for critical two-dimensional oriented percolation with V. Tassion and A. Teixeira, PTRF.

[35] Brochette percolation with M. Hilario, G. Kozma and V. Sidoravicius, Israel J. Math.

[34] Sharp phase transition for the random-cluster and Potts models via decision trees with A. Raoufi and V. Tassion Ann. Math. (2019).

[33] Universality for the random-cluster model on isoradial graphs with J.-H. Li and I. Manolescu. EJP (2018).

[32] The sharp threshold for the Duarte model with B. Bollobás, R. Morris and P. Smith, Ann. Prob. (2017).

[31] Exponential decay of loop lengths in the loop $ O (n) $ model with large $ n$ with R. Peled, W. Samotij, Y. Spinka, CMP (2017).

[30] Continuity of the phase transition for planar random-cluster and Potts models with $1\le q\le 4$ with V. Sidoravicius and V. Tassion, CMP (2017).

[29] Conformal invariance of crossing probabilities for the Ising model with free boundary conditions with S. Benoist and C. Hongler, Ann. IHP (2016).

[28] A new proof of the sharpness of the phase transition for Bernoulli percolation on $\mathbb Z^d$ with V. Tassion, Ens. Math. (2016).

[27] A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model with V. Tassion, CMP (2016).

[26] On the probability that self-avoiding walk ends at a given point with A. Glazman, A. Hammond, and I. Manolescu Ann. Prob. (2016).

[25] A quantitative Burton-Keane estimate under strong FKG condition with D. Ioffe and Y. Velenik, Ann. Prob. (2016).

[24] The phase transitions of the planar random-cluster and Potts models with $q\ge1$ are sharp with I.Manolescu, PTRF (2016).

[23] Crossing probabilities in topological rectangles for the critical planar FK-Ising model with D. Chelkak and C. Hongler, EJP (2016).

[22] Absence of infinite cluster for critical Bernoulli percolation on slabs with V. Sidoravicius and V. Tassion, CPAM (2016).

[21] Disorder, entropy and harmonic functions with I. Benjamini, G. Kozma and A. Yadin, Ann. Prob. (2015).

[20] Random currents and continuity of Ising model's spontaneous magnetization with M. Aizenman and V. Sidoravicius, CMP (2015).

[19] On the critical parameters of the $q\ge4$ random-cluster model on isoradial graphs with V. Beffara and S. Smirnov, J. Phys. A (2015).

[18] Convergence of Ising interfaces to Schramm's SLE curves with D. Chelkak, C. Hongler, A. Kemppainen and S. Smirnov, Comptes Rendus Math. (2014).

[17] The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is $1+\sqrt 2$ with N. Beaton, M. Bousquet-Mélou, J. De Gier and A. Guttmann, CMP (2014).

[16] Seven-dimensional forest fires with D. Ahlberg, G. Kozma and V. Sidoravicius, Ann. IHP (2014).

[15] The near-critical planar FK-Ising model with C. Garban and G. Pete, CMP (2014).

[14] Supercritical self-avoiding walks are space-filling with G. Kozma and A. Yadin, Ann. IHP (2014).

[13] On the Gibbs states of the noncritical Potts model on $\mathbb Z^2$ with L. Coquille, D. Ioffe and Y. Velenik, PTRF (2014).

[12] Self-avoiding walk is sub-ballistic with A. Hammond, CMP (2013).

[11] The critical temperature for the Ising model on planar doubly periodic graphs with D. Cimasoni, EJP (2013).

[10] Limit of the Wulff Crystal when approaching criticality for site percolation on the triangular lattice ECP (2013).

[9] Containing Internal Diffusion Limited Aggregation with C. Lucas, A. Yadin and A. Yehudayoff, ECP (2013).

[8] Sharp metastability threshold for an anisotropic bootstrap percolation model with A. C. D. van Enter, Ann. Prob. (2013).

[7] The connective constant of the honeycomb lattice equals $\sqrt{2+\sqrt 2}$ with S. Smirnov, Ann. Math. (2012).

[6] Divergence of the correlation length for critical planar FK percolation with $1\le q\le 4$ via parafermionic observables J. Phys. A (2012).

[5] The self-dual point of the two-dimensional random-cluster model is critical for $q\ge1$ with V. Beffara, PTRF (2012).

[4] The sharp threshold for bootstrap percolation in all dimensions with J. Balogh, B. Bollobás, and R. Morris, Trans. AMS (2012).

[3] Smirnov's fermionic observable away from criticality with V. Beffara, Ann. Prob. (2012).

[2] Connection probabilities and RSW-type bounds for the two-dimensional FK Ising model with C. Hongler, P. Nolin, CPAM (2011).

[1] Bridge decomposition of Restriction Measures with T. Alberts, J. Stat. Phys. (2010).

[72] Phase transition for the vacant set of random walk and random interlacements. with S. Goswami, P.-F. Rodriguez, F. Severo, A. Teixeira,, preprint.

[71] Finite range interlacements and couplings. with S. Goswami, P.-F. Rodriguez, F. Severo, A. Teixeira, preprint.

[70] Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules. with I. Hartarsky, preprint.

[69] Near critical scaling relations for planar Bernoulli percolation without differential inequalities. with I. Manolescu and V. Tassion, preprint.

[68] Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension $d\ge 3$. with A. Rivera, P.F. Rodriguez, and H. Vanneuville, preprint.

[67] Conformal invariance of double random currents I: identification of the limit with M. Lis and W. Qian, preprint.

[66] Conformal invariance of double random currents II: tightness and properties in the discrete with M. Lis and W. Qian, preprint.

[65] Rotational invariance in critical planar lattice models with K.K. Kozlowski, D. Krachun, I. Manolescu, and M. Oulamara, preprint.

[64] Delocalization of the height function of the six-vertex model with A. Karrila, I. Manolescu, and M. Oulamara, preprint.

[63] On the six-vertex model’s free energy with K.K. Kozlowski, D. Krachun, I. Manolescu, and T. Tikhonovskaia, preprint.

[62] Planar random-cluster model: scaling relations with I. Manolescu, preprint.

[61] Long-range order for critical Book-Ising and Book-percolation with C. Garban and V. Tassion, preprint.

[60] Long-range models in 1D revisited with C. Garban and V. Tassion, preprint.

[59] Logarithmic variance for the height function of square-ice with M. Harel, B. Laslier, A. Raoufi, G. Ray.

[58] Equality of critical parameters for percolation of Gaussian free field level-sets with S. Goswami, P.F. Rodriguez and F. Severo, Duke Mathematical Journal. (to appear).

[57] Existence of phase transition for percolation using the Gaussian Free Field with S. Goswami, A. Raoufi, F. Severo and A. Yadin,

*Duke Mathematical Journal*(to appear).[56] Upper bounds on the percolation correlation length with G.Kozma and V. Tassion,

*special volume in memory of Vladas Sidoravicius published in Birkhauser series "Progress in Probability" (to appear).*[55] Universality of two-dimensional critical cellular automata with B. Bollobás, R. Morris and P. Smith

*PLMS*(to appear).[54] Discontinuity of the phase transition for the planar random-cluster and Potts models with $q>4$ with M. Gagnebin, M. Harel, I. Manolescu and V. Tassion.

*Annales de l'ENS*.[53] Renormalization of crossing probabilities in the planar random-cluster model with V. Tassion.

*Dobrushin's issue of Moscow Math. journal*(to appear).[52] Planar random-cluster model: fractal properties of the critical phase with I. Manolescu and V. Tassion.

*PTRF*.[51] Marginal triviality of the scaling limits of critical 4D Ising and $\varphi_4^4$ models with M. Aizenman.

*Ann. Math.*[50] Macroscopic loops in the loop $O(n)$ model at Nienhuis' critical point with A. Glazman, R. Peled and Y. Spinka

*JEMS*.[49] A note on Schramm's locality conjecture for random-cluster models with V. Tassion

*Sojourns in Probability Theory and Statistical Physics - II*.[48] Subcritical phase of $d$-dimensional Poisson-Boolean percolation and its vacant set with A. Raoufi and V. Tassion

*AHL*.[47] On the number of maximal paths in directed last-passage percolation with H. Kesten, F. Nazarov, Y. Peres, V. Sidoravicius

*Ann. Probab.*.[46] Bounding the number of self-avoiding walks: Hammersley-Welsh with polygon insertion with S. Ganguly, A. Hammond and I. Manolescu

*AOP*.[45] Dimerization and Néel order in different quantum spin chains through a shared loop representation with M. Aizenman and S. Warzel.

*Annales de l'IHP D*.[44] Internal Diffusion-Limited aggregation with uniform starting points with I. Benjamini, G. Kozma and C. Lucas,

*AIHP*(to appear).[43] Exponential decay of truncated correlations for the Ising model in any dimension for all but the critical temperature with S. Goswami and A. Raoufi,

*CIMP*.[42] On the double random current nesting field with M. Lis,

*PTRF*.[41] Exponential decay of connection probabilities for subcritical Voronoi percolation in $\mathbb R^d$ with A. Raoufi and V. Tassion, PTRF.

[40] Minimal growth harmonic functions on lamplighter groups with I. Benjamini, G. Kozma and A. Yadin, New York J Math.

[39] Emergent Planarity in two-dimensional Ising Models with finite-range Interactions with M. Aizenman, V. Tassion and S. Warzel, Inventiones.

[38] A new computation of the critical point for the planar random-cluster model with $q\ge1$ with A. Raoufi and V. Tassion, Ann. IHP.

[37] Higher order corrections for anisotropic bootstrap percolation with A. C. D. van Enter and T. Hulshof, PTRF .

[36] The box-crossing property for critical two-dimensional oriented percolation with V. Tassion and A. Teixeira, PTRF.

[35] Brochette percolation with M. Hilario, G. Kozma and V. Sidoravicius, Israel J. Math.

[34] Sharp phase transition for the random-cluster and Potts models via decision trees with A. Raoufi and V. Tassion Ann. Math. (2019).

[33] Universality for the random-cluster model on isoradial graphs with J.-H. Li and I. Manolescu. EJP (2018).

[32] The sharp threshold for the Duarte model with B. Bollobás, R. Morris and P. Smith, Ann. Prob. (2017).

[31] Exponential decay of loop lengths in the loop $ O (n) $ model with large $ n$ with R. Peled, W. Samotij, Y. Spinka, CMP (2017).

[30] Continuity of the phase transition for planar random-cluster and Potts models with $1\le q\le 4$ with V. Sidoravicius and V. Tassion, CMP (2017).

[29] Conformal invariance of crossing probabilities for the Ising model with free boundary conditions with S. Benoist and C. Hongler, Ann. IHP (2016).

[28] A new proof of the sharpness of the phase transition for Bernoulli percolation on $\mathbb Z^d$ with V. Tassion, Ens. Math. (2016).

[27] A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model with V. Tassion, CMP (2016).

[26] On the probability that self-avoiding walk ends at a given point with A. Glazman, A. Hammond, and I. Manolescu Ann. Prob. (2016).

[25] A quantitative Burton-Keane estimate under strong FKG condition with D. Ioffe and Y. Velenik, Ann. Prob. (2016).

[24] The phase transitions of the planar random-cluster and Potts models with $q\ge1$ are sharp with I.Manolescu, PTRF (2016).

[23] Crossing probabilities in topological rectangles for the critical planar FK-Ising model with D. Chelkak and C. Hongler, EJP (2016).

[22] Absence of infinite cluster for critical Bernoulli percolation on slabs with V. Sidoravicius and V. Tassion, CPAM (2016).

[21] Disorder, entropy and harmonic functions with I. Benjamini, G. Kozma and A. Yadin, Ann. Prob. (2015).

[20] Random currents and continuity of Ising model's spontaneous magnetization with M. Aizenman and V. Sidoravicius, CMP (2015).

[19] On the critical parameters of the $q\ge4$ random-cluster model on isoradial graphs with V. Beffara and S. Smirnov, J. Phys. A (2015).

[18] Convergence of Ising interfaces to Schramm's SLE curves with D. Chelkak, C. Hongler, A. Kemppainen and S. Smirnov, Comptes Rendus Math. (2014).

[17] The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is $1+\sqrt 2$ with N. Beaton, M. Bousquet-Mélou, J. De Gier and A. Guttmann, CMP (2014).

[16] Seven-dimensional forest fires with D. Ahlberg, G. Kozma and V. Sidoravicius, Ann. IHP (2014).

[15] The near-critical planar FK-Ising model with C. Garban and G. Pete, CMP (2014).

[14] Supercritical self-avoiding walks are space-filling with G. Kozma and A. Yadin, Ann. IHP (2014).

[13] On the Gibbs states of the noncritical Potts model on $\mathbb Z^2$ with L. Coquille, D. Ioffe and Y. Velenik, PTRF (2014).

[12] Self-avoiding walk is sub-ballistic with A. Hammond, CMP (2013).

[11] The critical temperature for the Ising model on planar doubly periodic graphs with D. Cimasoni, EJP (2013).

[10] Limit of the Wulff Crystal when approaching criticality for site percolation on the triangular lattice ECP (2013).

[9] Containing Internal Diffusion Limited Aggregation with C. Lucas, A. Yadin and A. Yehudayoff, ECP (2013).

[8] Sharp metastability threshold for an anisotropic bootstrap percolation model with A. C. D. van Enter, Ann. Prob. (2013).

[7] The connective constant of the honeycomb lattice equals $\sqrt{2+\sqrt 2}$ with S. Smirnov, Ann. Math. (2012).

[6] Divergence of the correlation length for critical planar FK percolation with $1\le q\le 4$ via parafermionic observables J. Phys. A (2012).

[5] The self-dual point of the two-dimensional random-cluster model is critical for $q\ge1$ with V. Beffara, PTRF (2012).

[4] The sharp threshold for bootstrap percolation in all dimensions with J. Balogh, B. Bollobás, and R. Morris, Trans. AMS (2012).

[3] Smirnov's fermionic observable away from criticality with V. Beffara, Ann. Prob. (2012).

[2] Connection probabilities and RSW-type bounds for the two-dimensional FK Ising model with C. Hongler, P. Nolin, CPAM (2011).

[1] Bridge decomposition of Restriction Measures with T. Alberts, J. Stat. Phys. (2010).

Lecture notes

Lectures on the
Ising and Potts models on the hypercubic lattice PIMS summer
school (2017).
Introduction to percolation theory Master course in IHES.

Lectures on Planar percolation with a glimpse of Schramm Loewner Evolution with V. Beffara, Probab. Surveys (2013).

Conformal invariance of lattice models with S. Smirnov, Clay Summer School (2010).

Lectures on self-avoiding-walks with R. Bauerschmidt, J. Goodman, and G. Slade, Clay Summer School (2010).

Other publications

100 Years of
the (Critical) Ising Model on the Hypercubic Lattice. Proceedings
of the ICM (2022).

Parafermionic observables and their applications to planar statistical physics models Book, Ensaios Matematicos (2013).

Graphical representations of lattice spin models Book, Édition spartacus (2015).

Critical point and duality in planar lattice models with V. Beffara, Proceedings Probab. in St. Petersburg (2016).

The Bethe ansatz for the six-vertex and XXZ models: an exposition with M. Gagnebin, M. Harel, I. Manolescu and V. Tassion, Prob. Surveys (2018).

Sharp threshold phenomena in statistical physics Proceedings of the Takagi Lecture (2017).

Sixty years of percolation Proceedings of the ICM (2018).

Order/disorder phase transitions: the example of the Potts model Proceedings of Current Developments in math (2015).

Random currents expansion of the Ising model Proceedings of the 7th European Congress of Mathematicians in Berlin (2016).

RSW and Box-Crossing Property for Planar Percolation with V. Tassion, IAMP proceedings (2015).

A proof of first order phase transition for the planar random-cluster and Potts models with $q\gg1$ Proceedings of Stochastic Analysis on Large Scale Interacting Systems in RIMS kokyuroku Besssatu (2016).

Parafermionic observables and their applications IAMP bulletin (2016).

Phase transition in random-cluster and O(n)-models PhD Thesis (2011).

Law of the Iterated Logarithm for the random walk on the infinite percolation cluster Master Thesis (2008).

Parafermionic observables and their applications to planar statistical physics models Book, Ensaios Matematicos (2013).

Graphical representations of lattice spin models Book, Édition spartacus (2015).

Critical point and duality in planar lattice models with V. Beffara, Proceedings Probab. in St. Petersburg (2016).

The Bethe ansatz for the six-vertex and XXZ models: an exposition with M. Gagnebin, M. Harel, I. Manolescu and V. Tassion, Prob. Surveys (2018).

Sharp threshold phenomena in statistical physics Proceedings of the Takagi Lecture (2017).

Sixty years of percolation Proceedings of the ICM (2018).

Order/disorder phase transitions: the example of the Potts model Proceedings of Current Developments in math (2015).

Random currents expansion of the Ising model Proceedings of the 7th European Congress of Mathematicians in Berlin (2016).

RSW and Box-Crossing Property for Planar Percolation with V. Tassion, IAMP proceedings (2015).

A proof of first order phase transition for the planar random-cluster and Potts models with $q\gg1$ Proceedings of Stochastic Analysis on Large Scale Interacting Systems in RIMS kokyuroku Besssatu (2016).

Parafermionic observables and their applications IAMP bulletin (2016).

Phase transition in random-cluster and O(n)-models PhD Thesis (2011).

Law of the Iterated Logarithm for the random walk on the infinite percolation cluster Master Thesis (2008).