The notion of propagation of chaos for large systems of interacting particles originates in
statistical physics and has recently become a central notion in many areas of applied …

In this paper, we consider nonlinear diffusion processes driven by space-time white noises,
which have an interpretation in terms of partial differential equations. For a specific choice of …

The aim of this paper is to obtain estimates for the density of the law of a specific nonlinear
diffusion process at any positive bounded time. This process is issued from kinetic theory …

In this paper we introduce numerical schemes for a one-dimensional kinetic model of the
Boltzmann equation with dissipative collisions and variable coefficient of restitution. In …

We propose a collision-oriented particle system to approximate a class of Landau-type
equations. This particle system is formally derived from a particle system with random …

The standard d-dimensional parabolic--parabolic Keller--Segel model for chemotaxis
describes the time evolution of the density of a cell population and of the concentration of a …

We prove that any weak solution (in the sense of Desvillettes and Villani [6]) to the Landau
homogeneous equation is smooth and, in particular, that it lies in Schwartz space. Our result …

In this article, we propose a finite element discretization of the Boltzmann-Lorentz operator
for which it is possible to define a grazing collision limit. We illustrate this discretization by …

Using probabilistic tools, this work states a pointwise convergence of function solutions of
the 2-dimensional Boltzmann equation to the function solution of the Landau equation for …

The aim of this paper is to show how a probabilistic approach and the use of Malliavin
calculus provide exponential estimates for the solution of a spatially homogeneous Landau …