A mean-field limit for the Vlasov-Poisson system

Derivation of the Vlasov-Poisson equation from Newtonian mechanics of interacting particles is challenging in the case of singular interactions.

In the talk I will present a new method which is based on probabilistic arguments and allows to consider Coulomb interactions with an N-dependent cut-off. In particular, I will show convergence of the empirical distribution to solutions of the Vlasov-Poisson equation for typical initial conditions.