Large deviations for interacting multiscale particle systems

TL;DR

This paper establishes a large deviations principle for a system of interacting particles in a multiscale environment, characterizing rare events in the combined limit of many particles and fast time-scale separation.

Contribution

It introduces a novel weak convergence approach to derive the large deviations rate function for multiscale particle systems, including cases with measure-dependent diffusion matrices.

Findings

Derived a representation for the large deviations rate function.

Characterized effective controlled mean field dynamics.

Extended results to systems with measure-dependent diffusion matrices.

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 simultaneously. 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 obtain equivalent representations for the large deviations rate function of the form of Dawson-G\"artner which hold even in the case where the diffusion matrix depends on the empirical measure and when the particles undergo averaging in addition to the propagation of chaos.