The goal of this review paper is to provide the reader with a concise introduction to the
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

It is well known that the analysis of the large-time asymptotics of Fokker-Planck type
equations by the entropy method is closely related to proving the validity of convex Sobolev …

In this paper, we find optimal constants of a special class of Gagliardo–Nirenberg type
inequalities which turns out to interpolate between the classical Sobolev inequality and the …

The title of this book already says something about its contents and historical origin, but
since it is meant in a rigorous mathematical context, a few words of explanation may be …

We present and discuss various one-dimensional linear Fokker–Planck-type equations that
have been recently considered in connection with the study of interacting multi-agent …

We study the long‐time behavior of kinetic equations in which transport and spatial
confinement (in an exterior potential or in a box) are associated with a (degenerate) collision …

We study sampling from a target distribution $\nu_*= e^{-f} $ using the unadjusted Langevin
Monte Carlo (LMC) algorithm. For any potential function $ f $ whose tails behave like …

The aim of this survey is to serve as an introduction to the different techniques available in
the broad field of aggregation-diffusion equations. We aim to provide historical context, key …

Both experimental and numerical studies of fluid motion indicate that initially localized
regions of vorticity tend to evolve into isolated vortices and that these vortices then serve as …