Speaker: Wenpin Tang, IEOR Department at Columbia Engineering

Title: Phase transition in mean field models

Abstract: In this talk, I will discuss two mean field models in which a certain phase transition occurs. I first describe McKean-Vlasov equations involving hitting times which arise as the mean field limit of particle systems with annihilation. One such example is the super-cool Stefan problem. It is well known that such a system may have blow-ups. We provide some sufficient conditions on the model data to assure either blow-ups or no blow-ups. In the second part, I will discuss the convergence rate of second order mean-field games to first order ones, motivated from numerical challenges in first order mean field PDEs and the weak noise theory in KPZ universality. When the Hamiltonian and the coupling function have a certain growth, the rate is independent of the dimension; on the other hand, the rate decays in dimension (curse of dimensionality) when the Hamiltonian and the coupling function have small growth. These are based on joint work with Yuming Paul Zhang.

Bio: Wenpin Tang is an Assistant Professor at Department of Industrial Engineering and Operations Research, Columbia University. Before joining Columbia IEOR, he was a postdoctoral researcher at Department of Industrial Engineering and Operations Research, UC Berkeley, and an assistant adjunct professor at Department of Mathematics, UCLA. He obtained a Ph.D. from Department of Statistics, UC Berkeley, and an engineer diploma from Ecole Polytechnique, France. His research lies at the intersection of probability theory, machine learning and financial technology.

This talk will be offered in a hybrid format. Please send an email to [email protected] for the Zoom link.