Speaker Introduction

Lim joined Xiamen University Malaysia in September 2020. He earned his PhD (in mathematics) from the University of Wisconsin-Madison. His primary research interest is PDEs and probability, particularly how PDEs arise from a probabilistic model, and the connection/application in between.
 

Abstract

Interacting particle systems describe the collective evolution of a large number of particles whose dynamics are governed by underlying Markov processes. A prototypical example is the McKean–Vlasov diffusion, which can be viewed as the superposition of an independent diffusion component and an interaction term in the drift that depends on the empirical distribution (or mean field) of the system. An interesting phenomenon arising in such models is the propagation of chaos, which asserts that as the number of particles tends to infinity, any finite subset of particles becomes asymptotically independent, each following the law of the corresponding mean-field limit. A powerful tool for analysing this phenomenon is the coupling method, which provides a probabilistic framework to compare the evolution of interacting particles with their mean-field counterparts. The key idea is to construct a joint realisation of the two Markov processes in an efficient way that minimises their expected discrepancy, leading naturally to the concept of optimal couplings of Markov processes. In this talk, we begin with interacting particle systems and show how the notion of optimal coupling emerges from their analysis, before turning to recent developments on optimal couplings for Lévy processes.