A gradient flow approach of propagation of chaos

Abstract

We provide an estimation of the dissipation of the Wasserstein 2 distance between the law of some interacting \begin{document}$ N $\end{document} -particle system, and the \begin{document}$ N $\end{document} times tensorized product of the solution to the corresponding limit nonlinear conservation law. It then enables to recover classical propagation of chaos results [ 20 ] in the case of Lipschitz coefficients, uniform in time propagation of chaos in [ 17 ] in the case of strictly convex coefficients. And some recent results [ 7 ] as the case of particle in a double well potential.