The Kardar–Parisi–Zhang (KPZ) equation is conjectured to universally describe the
fluctuations of weakly asymmetric interface growth. Here we provide the first intrinsic well …

ASEP(q,j) converges to the KPZ equation Page 1 www.imstat.org/aihp Annales de l’Institut
Henri Poincaré - Probabilités et Statistiques 2018, Vol. 54, No. 2, 995–1012 https://doi.org/10.1214/17-AIHP829 …

We consider a system of infinitely many interacting Brownian motions that models the height
of a one-dimensional interface between two bulk phases. We prove that the large scale …

We obtain the large scale limit of the fluctuations around its hydrodynamic limit of the density
of particles of a weakly asymmetric exclusion process in dimension up to three. The proof is …

We study the equilibrium fluctuations of an interacting particle system evolving on the
discrete ring with three species of particles that we name $ A, B $ and $ C $, but at each site …

A microscopic model of interacting oscillators, which admits two conserved quantities,
volume, and energy, is investigated. We begin with a system driven by a general nonlinear …

These lecture notes, adapted from the habilitation thesis of the author, survey in a first part
various exact results obtained in the past few decades about KPZ fluctuations in one …

We consider the weakly asymmetric simple exclusion process on the discrete space {1,⋯, n-
1}(n∈ ℕ), in contact with stochastic reservoirs, both with density ρ∈(0, 1) at the extremity …

We consider the facilitated exclusion process, an interacting particle system on the integer
line where particles hop to one of their left or right neighbouring site only when the other …

We consider one-dimensional exclusion processes with long jumps given by a transition
probability of the form pn (⋅)= s (⋅)+ γ na (⋅), such that its symmetric part s (⋅) is irreducible …