Title: Weakly interacting particle systems on graphs and their applications

Abstract: Weakly interacting particle systems consist of a collection of stochastic processes interacting with others in the mean-field manner, where the evolution of a particle depends on its own state and the empirical distribution of all particles in the system. The large population limit is described by independent McKean--Vlasov processes. In this talk, we present recent study of asymptotic behavior of weakly interacting particles on dense heterogeneous graphs, where the system consists of a large number of nodes and the state of each node is described by a stochastic process with locally mean-field type interactions. Law of large numbers and propagation of chaos properties are established. Applications in large queueing networks and deep neural networks will also be briefly discussed.