Propagation of chaos for the Vlasov-Poisson-Fokker-Planck equation with a polynomial cut-off

We consider a N-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system. Taking the cut-off like N-delta with delta < 1/d in the force, we provide a quantitative error estimate between the empirical measure associated to that N-particle system and the solutions of the d-dimensional Vlasov-Poisson-Fokker-Planck (VPFP) system. We also study the propagation of chaos for the Vlasov-Fokker-Planck equation with less singular interaction forces than the Newtonian one.