Large deviations for interacting multiscale particle systems

Understand

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.