Mean field limit for stochastic particle systems

Abstract

We review some classical and more recent results for the derivation of mean field equations from systems of many particles, focusing on the stochastic case where a large system of SDEs leads to a McKean–Vlasov PDE as the number N of particles goes to infinity. Classical mean field limit results require that the interaction kernel be essentially Lipschitz. To handle more singular interaction kernels is a long-standing and challenging question but which has had some recent successes.