Large deviations for interacting multiscale particle systems
Spiliopoulos, Konstantinos; Bezemek, Zachary
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 in certain special cases equivalent representations for the large
deviations rate function.
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