My research interests lie in the application of probability theory to problems originating from statistical physics. Here are some topics I am/have been working on:
study of correlation functions and of the correlation length in lattice spin models (such as Ising, Potts or XY models),
mixing properties of lattice models and their link with analytic properties,
scaling limit of interfaces in two dimensional lattice models.
Yacine Aoun, Pietro Caputo, Moritz Dober, Alessandro Giuliani, Alexander Glazman, Dmitry Ioffe, Piet Lammers, Florian Schweiger, Assaf Shapira, Senya Shlosman, Yvan Velenik, Vitali Wachtel
[19] Quantitative delocalization for solid-on-solid models at high temperature and arbitrary tilt
joint with F. Schweiger, arXiv
[18] Discontinuous transition in 2D Potts: I. Order-Disorder Interface convergence
joint with M. Dober, and A. Glazman, arXiv
[17] A new perspective on the equivalence between Weak and Strong Spatial Mixing in two dimensions
[16] Relaxation time and topology in 1D O(N) models
joint with P. Caputo, and A. Shapira, J. Stat. Phys. 192, 96 (2025), arXiv
[15] Fixed-magnetization Ising model with a slowly varying magnetic field
joint with Y. Aoun, and Y. Velenik, J. Stat. Phys. 191, 125 (2024), arXiv
[14] Low temperature asymptotic expansion for classical O(N) vector models
joint with A. Giuliani, Probability and Mathematical Physics 6-2 (2025), 439--477, arXiv
[13] On the two-point function of the Potts model in the saturation regime
joint with Y. Aoun, and Y. Velenik, Comm. Math. Phys. (2022), arXiv
[12] Ornstein-Zernike behavior for Ising models with infinite-range interactions
joint with Y. Aoun, and Y. Velenik, Annales de l'Institut Henri Poincaré 60, 167-207 (2024), arXiv
[11] Failure of Ornstein-Zernike asymptotics for the pair correlation function at high temperature and small density
joint with Y. Aoun, D. Ioffe, and Y. Velenik, Physical Review E 103, L050104 (2021), arXiv
[10] Delocalisation and absolute-value-FKG in the solid-on-solid model
joint with P. Lammers, Probab. Theory Relat. Fields (2023), arXiv
[9] Critical prewetting in the 2d Ising model
joint with D. Ioffe, S. Shlosman, and Y. Velenik, Annals of Probability 50, 1127-1172 (2022), arXiv
[8] Non-analyticity of the correlation length in systems with exponentially decaying interactions
joint with Y. Aoun, D. Ioffe, and Y. Velenik, Commun. Math. Phys. 386, 433-467 (2021), arXiv
[7] Existence and properties of connections decay rate for high temperature percolation models
Electron. J. Probab. 27, 1-19 (2022), arXiv
[6] Weak mixing and analyticity in Random Cluster and low temperature Ising models
[5] Invariance principle for a Potts interface along a wall
joint with D. Ioffe, Y. Velenik and V. Wachtel, J. Stat. Phys. 180, 832-861 (2020) (special issue celebrating Joel Lebowitz' 90th birthday), arXiv
[4] Weak Mixing and Analyticity of the Pressure in the Ising Model
Commun. Math. Phys. 377, 675–696 (2020), arXiv
[3] Sharp Asymptotics for the Truncated Two-Point Function of the Ising Model with a Positive Field
Commun. Math. Phys. 374, 1361–1387 (2020), arXiv
[2] Asymptotics of Even-Even Correlations in the Ising Model
joint with Y. Velenik, Probab. Theory Relat. Fields 175, 309-340 (2019), arXiv
[1] Potts Models with a Defect Line
joint with Y. Velenik, Commun. Math. Phys. 362, 55-106 (2018), arXiv
[3] A note on the renormalization group approach to the Central Limit Theorem
[2] Intermediate Fluctuations in the Ising Model
joint with S. Shlosman, and Y. Velenik, Markov Processes And Related Fields (2024)
[1] Asymptotics of correlations in the Ising model: a brief survey
joint with Y. Velenik, Panoramas et Synthèses 59, 157-184 (2023), arXiv
You can also find all my publications on arXiv, and my Ph.D. thesis is available here.
ORCID, and Google scholar profiles.
May 2025, Bernoulli center (EPFL), Workshop "Walk Spin Loop Field"
April 2025, University of Geneva, Geneva Mathematical Physics Seminar
February 2025, Diablerets, Workshop on statistical mechanic
February 2025, EPFL, Probability Seminar
January 2025, Geneva, Workshop
June 2024, Paris, Stat-Mech in Créteil 2024-II : Random Systems
November 2023, One World Mathematical Physic seminar (webinar)
February 2023, Università Roma Tre, conference "Universality in Condensed Matter and Statistical Mechanics"
October 2022, Percolation Today (webinar)
September 2022, Oberwolfach, Workshop "Large Scale Stochastic Dynamics"
June 2022, Technion, Haifa, Challenges in Probability and Statistical Mechanics
December 2021, Università Roma Tre, Mathematical Physic Seminar
July 2021, Statistical Mechanics: Recent Results, Workshop at IME-USP (online), Slides
June 2021, Bristol-Queen Mary-Warwick Probability Seminar (online), Slides
June 2021, Vienna Probability Seminar (online), Slides
May 2021, Percolation Today (webinar)
April 2021, Séminaire de probabilités de Marseille (online)
February 2021, Università Roma Tre, Mathematical Physic Seminar (online), Slides
November 2020, Percolation Today (webinar), Slides
September 2020, Porquerolles, Workshop "Random Polymers and Networks"
June 2020, Technische Universität München, Colloquium in probability (online), Slides
November 2019, Université de Fribourg, Probability Seminar
March 2019, Università Roma Tre, Mathematical Physic Seminar
November 2018, ETH Zurich, Seminar on Stochastic Processes
September 2018, Oberwolfach, Scaling Limits in Models of Statistical Mechanics Workshop
November 2017, Institut Fourier, Grenoble, Probability Seminar
November 2017, Université de Genève, Graduate Colloquium
May 2017, Université de Genève, Graduate Seminar