This paper is devoted to establish quantitative and qualitative estimates related to the notion
of chaos as firstly formulated by M. Kac [41] in his study of mean-field limit for systems of N …

We investigate the behavior in $ N $ of the $ N $--particle entropy functional for Kac's
stochastic model of Boltzmann dynamics, and its relation to the entropy function for solutions …

Nous étudions un système sur réseau à variable de spin continue. Dans la première partie,
nous établissons deux résultats abstraits: des conditions suffisantes pour une inégalité de …

In this work we derive local gradient and Laplacian estimates of the Aronson–Bénilan and Li–
Yau type for positive solutions of porous medium equations posed on Riemannian manifolds …

We present the derivation of the hydrodynamic limit under Eulerian scaling for a general
class of one-dimensional interacting particle systems with two or more conservation laws …

We consider a noninteracting unbounded spin system with conservation of the mean spin.
We derive a uniform logarithmic Sobolev inequality (LSI) provided the single-site potential is …

In this paper we consider the stochastic six-vertex model on a cylinder with arbitrary initial
data. First, we show that it exhibits a limit shape in the thermodynamic limit, whose density …

We investigate the behavior of the Gibbs-Shannon entropy of the stationary nonequilibrium
measure describing a one-dimensional lattice gas, of L sites, with symmetric exclusion …

Consider the asymmetric nearest-neighbor exclusion process (ASEP) on ${\mathbb Z} $ with
single particle drift $\gamma> 0$, starting from a Bernoulli product invariant measure …

We present a new approach to prove the macroscopic hydrodynamic behaviour for
interacting particle systems, and as an example we treat the well-known case of the …