A Mean Field Limit for the Vlasov–Poisson System

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 + ϵ . 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.