A NEW APPROACH TO THE MEAN-FIELD LIMIT OF VLASOV–FOKKER–PLANCK EQUATIONS

We introduce a novel approach to the mean-field limit of stochastic systems of interacting particles, leading to the first ever derivation of the mean-field limit to the Vlasov–Poisson–Fokker–Planck system for plasmas in dimension 2 together with a partial result in dimension 3. The method is broadly compatible with second-order systems that lead to kinetic equations and it relies on novel estimates on the BBGKY hierarchy. By taking advantage of the diffusion in velocity, those estimates bound weighted L^p norms of the marginals or observables of the system, uniformly in the number of particles. This allows us to qualitatively derive the mean-field limit for very singular interaction kernels between the particles, including repulsive Poisson interactions, together with quantitative estimates for a general kernel in L².