MCKEAN-VLASOV LIMIT FOR INTERACTING RANDOM-PROCESSES IN RANDOM-MEDIA

We apply large-deviation theory to particle systems with a random mean -field interaction in the McKean-Vlasov limit. In particular, we descr ibe large deviations and normal fluctuations around the McKean-Vlasov equation. Due to the randomness in the interaction, the McKean-Vlasov equation is a collection of coupled PDEs indexed by the state space of the single components in the medium. As a result, the study of its so lution and of the finite-size fluctuation around this solution require s some new ingredient as compared to existing techniques for nonrandom interaction.