In this talk, we will show concentration inequalities,  exponential convergence in the Wasserstein metric $W_{1}$, and uniform-in-time propagation of chaos for the mean-field weakly interacting particle system related to McKean-Vlasov equation. By means of the known approximate componentwise reflection coupling and with the help of some new cost function, we obtain explicit estimates for those three problems, avoiding the technical conditions in the known results. Our results apply to possibly multi-well confinement potentials, and interaction potentials $W$ with bounded second mixed derivatives $\nabla^2_{xy}W$ which are not too big, so that there is no phase transition. Several examples are provided to illustrate the results.  This is a joint work with L. Wu and C. Zhang.

学术海报.pdf