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 …

In this paper, we consider a mean-field stochastic differential equation, also called the
McKean–Vlasov equation, with initial data (t,x)∈0,T*R^d, whose coefficients depend on …

We derive quantitative estimates proving the propagation of chaos for large stochastic
systems of interacting particles. We obtain explicit bounds on the relative entropy between …

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 …

New weak and strong existence and weak and strong uniqueness results for the solutions of
multi-dimensional stochastic McKean–Vlasov equation are established under relaxed …

We consider general stochastic systems of interacting particles with noise which are relevant
as models for the collective behavior of animals, and rigorously prove that in the mean-field …

Abstract We develop Random Batch Methods for interacting particle systems with large
number of particles. These methods use small but random batches for particle interactions …

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 …