N-particle approximation to the nonlinear Vlasov–Poisson system

We present a new and elementary method for showing that every continuously differentiable distribution function which solves the (unmodified) Vlasov-Poisson system of stellar dynamics or plasma physics is the limit of discrete distributions induced by particles solving the differential equations of the N-body problem with modified force or electrical field, as simultaneously the number N of the particles tends to infinity and the modification parameter of the 1/r-singularity of the potential goes to zero. The method also allows the derivation of convergence rates.