A mean field limit for the Vlasov-Poisson system

Abstract

We present a probabilistic proof of the mean field limit and propagation of chaos $N$-particle systems in three dimensions with positive (Coulomb) or negative (Newton) $1/r$ potentials scaling like $1/N$ and an $N$-dependent cut-off which scales like $N^{-1/3+\epsilon }$. In particular, for typical initial data, we show convergence of the empirical distributions to solutions of the Vlasov-Poisson system with either repulsive electrical or attractive gravitational interactions.

Final, submitted version: Improved convergence rate, improved presentation, error corrections, added acknowledgements