Sharp propagation of chaos for mean field Langevin dynamics, control, and games

We establish the sharp rate of propagation of chaos for McKean-Vlasov equations with coefficients that are non-linear in the measure argument, i.e., not necessarily given by pairwise interactions. Results are given both on bounded time horizon and uniform in time. As applications, we deduce the sharp rate of propagation of chaos for the convergence problem in mean field games and control, and for mean field Langevin dynamics, the latter being uniform in time in the strongly displacement convex regime. Our arguments combine the BBGKY hierarchy with techniques from the literature on weak propagation of chaos.