Scaling Limit of Moderately Interacting Particle Systems with Singular Interaction and Environmental Noise

Abstract

We consider moderately interacting particle systems with singular interaction kernel and environmental noise. It is shown that the mollified empirical measures converge in strong norms to the unique (local) solutions of nonlinear Fokker-Planck equations. The approach works for the Biot-Savart and repulsive Poisson kernels.

40 pages. Accepted by Annals of Applied Probability

References in corpus (1)

• A particle system approach to aggregation phenomena

Cited by in corpus (1)

• Scaling Limits of Stochastic Transport Equations on Manifolds