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 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 …

This book gives an exposition of the principal concepts and results related to second order
elliptic and parabolic equations for measures, the main examples of which are Fokker …

Now back in print by the AMS, this is a significantly revised edition of a book originally
published in 1987 by Academic Press. This book gives the reader an introduction to the …

We consider ${\mathbb {R}}^ d $-valued diffusion processes of type\begin {align*} dX_t\=\b
(X_t) dt+ dB_t.\end {align*} Assuming a geometric drift condition, we establish contractions of …

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 …

In this paper, we provide an analytical framework for investigating the efficiency of a
consensus-based model for tackling global optimization problems. This work justifies the …

We consider conservative and gradient flows for N-particle Riesz energies with meanfield
scaling on the torus Td, for d 1, and with thermal noise of McKean–Vlasov type. We prove …

We consider a stochastic system of N particles, usually called vortices in that setting,
approximating the 2D Navier–Stokes equation written in vorticity. Assuming that the initial …

We describe conditions on non-gradient drift diffusion Fokker–Planck equations for its
solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance …