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 …

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 …

We consider stochastic dynamic games in large population conditions where multiclass
agents are weakly coupled via their individual dynamics and costs. We approach this large …

This book grew out of the lecture notes I prepared for a graduate class I taught at Princeton
University in 2011–12, and again in 2012–13. My goal was to introduce the students to …

We establish quantitative concentration estimates for the empirical measure of many
independent variables, in transportation distances. As an application, we provide some error …

We use here a particle system to prove both a convergence result (with convergence rate)
and a deviation inequality for solutions of granular media equation when the confinement …

We introduce a new interacting particle system to investigate the behavior of the nonlinear,
nonlocal diffusive equation already studied by Benachour et al.[3, 4]. We first prove an …

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 …

The aim of this paper is to study the behavior of solutions of some nonlinear partial
differential equations of Mac Kean–Vlasov type. The main tools used are, on one hand, the …

We address the long time behaviour of weakly interacting diffusive particle systems on the d-
dimensional torus. Our main result is to show that, under certain regularity conditions, the …