Mean-Field limits for Coulomb-type dynamics

Sylvia Serfaty studies the many-particle limit of systems driven by Coulomb or Riesz interactions through gradient flows or analogous conservative dynamics, possibly with added random diffusion. The Riesz interaction has inverse-distance exponent s between d−2 and d in dimension d. The talk presents convergence, as the number of particles tends to infinity, to the expected mean-field evolution. It also discusses deriving the Vlasov–Poisson equation from Newtonian dynamics in the monokinetic case and related results for Ginzburg–Landau vortex dynamics.