In this talk, we will show the gradient estimate of the Poisson equation, the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$ 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 when the confinement potential $V$ has many wells, the interaction potential $W$ has bounded second mixed derivative $/nabla^2_{xy}W$ which should be not too big so that there is no phase transition. As application, we obtain the concentration inequality of the mean-field interacting particle system with explicit constant, uniform in time. Several examples are provided to illustrate these results. This is a joint work with Prof. Liming Wu and Dr. Chaoen Zhang

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