Young Researchers Workshop: Stochastic and deterministic methods in kinetic theory

Mean field limit for stochastic particle systems with singular forces

Zhenfu Wang

University of Pennsylvania
[SLIDES]

Abstract:

We consider large systems of particles interacting through rough interaction kernels. We are able to control the relative entropy between the N-particles distribution and the expected limit which solves the corresponding McKean-Vlasov PDE. This implies the Mean Field limit to the McKean-Vlasov system together with Propagation of Chaos through the strong convergence of all the marginals. The method works at the level of the Liouville equation and relies on precise combinatorics results. By a careful truncation of the Biot-Savart kernel $K$, we can also provide an explicit convergence rate for stochastic vortex model approximating 2D Navier-Stokes equation. Joint work with Pierre-Emmanuel Jabin.