Sébastien Gouëzel, Université de Rennes 1, France

Title:``Large deviations for random walks without moment conditions on hyperbolic spaces''.Abstract: Consider a random walk on a hyperbolic space (the talk will mostly focuss on the special case of trees). It is known that the walk is converging almost surely…

Cécilia Lancien, Université Grenoble Alpes , France

Title: ``Quantum expander graphs''   Abstract: The goal of the talk will be to understand what quantum expander graphs are, what they are useful for, and how they can be constructed. We will first recall the definition of classical expander…

Marcin Lis, University of Vienna, Austria

Title: ``An elementary proof of phase transition in the planar XY model''.   Abstract: Using elementary methods we obtain a power-law lower bound on the two-point function of the planar XY spin model at low temperatures. This was famously first…

Jianping Jiang, Tsinghua University, China

Title: ``Ising model with various perturbations''. Abstract: We consider the behavior of the critical Ising model under various perturbations. In two dimensions, we focus on the particle masses associated with the near-critical scaling limit of the model with an external…

Yijun Wan, Ecole Normale Supérieure de Paris, France

Title: ``On the massive loop-erased random walks and massive SLEs''. Abstract: The last decade has witnessed numerous breakthroughs in establishing rigorously the conformal invariance of some statistical models at the critical temperature, largely due to the introduction of SLEs, Schramm…

Soufiane Hayou, National University of Singapore

Title: ``Some Insights from Neural Networks with Infinite Number of Parameters.'' Abstract: The theoretical analysis of infinite-width neural networks has led to many interesting practical results (choice of initialization schemes, choice of Bayesian priors etc.). However, the traditional infinite-width framework focuses…

Roland Bauerschmidt, University of Cambridge, UK

Title: ``Log-Sobolev inequality for near-critical Ising models''. Abstract: For ferromagnetic Ising models, we show that the log-Sobolev constant satisfies a simple bound expressed only in terms of the susceptibility of the model. This bound implies very generally that the log-Sobolev…

Domenico Marinucci, Università di Roma Tor Vergata, Italy

Title: ``The Geometry of Time-Dependent Spherical Random Fields''. Abstract: The investigation of the behaviour for geometric functionals of random fields on manifolds has drawn recently considerable attention. In this talk, we will review some of the existing literature and then…

Barbara Dembin, ETH Zürich, Switzerland

Title: ``Coalescence of geodesics and the BKS midpoint problem in first-passage percolation.'' Abstract:  We consider first-passage percolation on Z^2 with independent and identically distributed weights. Under the assumption that the limit shape has at least 32 extreme points, we prove that…

Reda Chhaibi, Université Paul Sabatier, France

Title: ``Free Probability for predicting the performance neural networks". Abstract: Gradient descent during the learning process of a neural network can be subject to many instabilities. The spectral density of the Jacobian is a key component for analyzing stability. Following…

Simona Diaconu, Stanford University, USA

Title: ``Method of Moments and Edge Eigenvalues.'' Abstract: The method of moments is a classical technique for showing weak convergence and follows a simple recipe: for any natural number m; compute the mth moments of the random variables of interest,…

Mauro Mariani, HSE University

Title: ``Metastable regimes of diffusion processes''. Abstract: I will discuss a classical example featuring a metastable behavior: finite-dimensional diffusion processes in the vanishing noise limit. Exponential estimates were introduced fifty years ago by Freidlin and Wentzell. Recent developments in potential…