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 …

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 …

We prove the mean field limit and quantitative estimates for many-particle systems with
singular attractive interactions between particles. As an important example, a full rigorous …

In this work we show the strong convergence of propagation of chaos for the particle
approximation of McKean-Vlasov SDEs with singular-interactions as well as for the …

In this note, we propose a modulated free energy combination of the methods developed by
P.-E. Jabin and Z. Wang [Inventiones (2018)] and by S. Serfaty [Proc. Int. Cong. Math.(2018) …

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 are interested in the two-dimensional Keller–Segel partial differential equation. This
equation is a model for chemotaxis (and for Newtonian gravitational interaction). When the …

Let $ d\geq 2$. In this paper, we investigate the following stochastic differential equation
(SDE) in ${\mathbb R}^ d $ driven by Brownian motion $${\rm d} X_t= b (t, X_t){\rm d} t+\sqrt …

The n particle system associatedwith (1) are described by the follow-ing SDEs,(5) dZ=
adB+(n--1)-,(V+/-G)(Z--Z) dt, lin, where (B.,..., B.) isa 2n-dimensional Brownian motion. Since …

We consider the asymptotic behaviour of the fluctuations for the empirical measures of
interacting particle systems with singular kernels. We prove that the sequence of fluctuation …