Analysis Seminar

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.