IISER MOHALI

Abstract: This talk analyzes the behavior of mean field models when the associated McKean-Vlasov equation has multiple equilibria. We leverage some tools from large deviations theory to study this situation. We first show a dynamical large deviation principle (LDP) for the mean field process. The rate function for this LDP admits a relative entropy form, and it quantifies the decay rate of the probabilities of rare events associated with the mean field process. We then transfer this LDP to the stationary regime and obtain precise asymptotics for the stationary behavior. The rate function is governed by the Freidlin-Wentzell quasipotential, which describes the cost of movement between various points in the state space. The global minimizers of the quasipotential quantify the stationary behaviour of the mean field process. Finally, we mention a few variations of the mean field model and discuss some open questions.

Tea: 05:00 PM