Probability

In this talk we discuss some results describing the fluctuation scaling limits for some interacting particle systems.

Dimer models (random lozenge or domino tilings) on large planar domains exhibit universality behavior: local convergence to translation-invariant Gibbs measures, global fluctuations described by the Gaussian Free Field (GFF), and Airy line ensemble at the edges. In this talk, I discuss two…

In this talk, we consider the asymmetric simple exclusion process with open boundaries (open ASEP). We give an overview on recent results on mixing times for the open ASEP. In particular, we discuss mixing times for the open ASEP at the triple point.

This talk is based on joint work with…

We study uniformly random lozenge tilings of polygonal domains as a model of random stepped surfaces, encoded by their height functions. Our analysis relies on an exact correspondence between vertical sections of the tiling and discrete beta-ensembles with repulsive interactions, providing a…

Sparse random graphs are widely viewed as discrete models of chaotic physical systems. Heuristically, this suggests that eigenvectors of the adjacency operator should exhibit Gaussian statistics. We prove that a broad class of random graphs, including both random regular graphs and irregular…

We consider the problem of efficiently optimizing random (spherical or Ising) perceptron models with general bounded Lipschitz activation. We focus on a class of algorithms with Lipschitz dependence on the disorder: this includes gradient descent, Langevin dynamics, approximate message passing,…

We study a natural one-parameter family of random bipolar-oriented planar maps which lies in the $\gamma$-Liouville quantum gravity (LQG) universality class for $\gamma \in (0, \sqrt{4/3}]$. For these maps, we identify exact scaling exponents for directed graph distances. Writing $n$ for the…

The Toda lattice is a particle system of classical mechanics, discovered by Toda in 1967. Due to its integrability, the Toda lattice with N particles possesses N independent conserved quantities. In this work, we show that under a certain class of random initial data with a constant particle…

The Toda lattice is a particle system of classical mechanics, discovered by Toda in 1967. Due to its integrability, the Toda lattice with N particles possesses N independent conserved quantities. In this work, we show that under a certain class of random initial data with a constant particle…

In joint work with Diederik van Engelenburg, Romain Panis and Franco Severo, we study the probability that the origin is connected to the boundary of the box of size n (the one-arm probability) in several percolation models related to the Ising model. We prove that different universality classes…