Large deviations for interacting multiscale particle systems

Abstract

We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles’ positions in the combined limit as the number of particles grow to infinity and the time-scale separation parameter goes to zero. We make use of weak convergence methods providing a convenient representation for the large deviations rate function, which allow us to characterize the effective controlled mean field dynamics. In addition, we rigorously obtain equivalent non-variational representations for the large deviations rate function as introduced by Dawson–Gärtner.