Large deviations for interacting multiscale particle systems

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