Sylvia Serfaty

Courant Institute

Mean-Field limits for Coulomb-type dynamics

We consider a system of \(N\) particles evolving according to the gradient flow of their Coulomb or Riesz interaction, or a similar conservative flow, and possible added random diffusion. By Riesz interaction, we mean inverse power \(s\) of the distance with \(s\) between \(d-2\) and \(d\) where \(d\) denotes the dimension. We present a convergence result as \(N\) tends to infinity to the expected limiting mean field evolution equation. We also discuss the derivation of Vlasov–Poisson from newtonian dynamics in the monokinetic case, as well as related results for Ginzburg–Landau vortex dynamics.