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 …

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 …

The description of emerging collective phenomena and self-organization in systems
composed of large numbers of individuals has gained increasing interest from various …

This is the first comprehensive introduction to the theory of mass transportation with its many—
and sometimes unexpected—applications. In a novel approach to the subject, the book both …

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 …

The long-time asymptotics of certain nonlinear, nonlocal, diffusive equations with a gradient
flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and …

We review some classical and more recent results for the derivation of mean field equations
from systems of many particles, focusing on the stochastic case where a large system of …

An algebraic decay rate is derived which bounds the time required for velocities to
equilibrate in a spatially homogeneous flow-through model representing the continuum limit …

Abstract We study the McKean–Vlasov equation ∂ _t ϱ= β^-1 Δ ϱ+ κ\, ∇ ⋅\,(ϱ ∇ (W ⋆
ϱ)),∂ t ϱ= β-1 Δ ϱ+ κ∇·(ϱ∇(W⋆ ϱ)), with periodic boundary conditions on the torus. We …

We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear
nonlocal equations with a gradient flow structure. These properties allow for accurate …