Event Date Details:
Refreshments served at 3:15 p.m.
- CFMAR Seminar Series
Title: Infinite-dimensional SDE related to random matrices — finite particle approximation and the density preserving property
Abstract: We consider infinite-dimensional SDE (ISDE) describing interacting Brownian motions in infinite dimensions. Mainly, we take up Dyson's Brownian motion with infinitely many particles. Dyson's Brownian motion, which is closely related to random matrices, is one of the most important ISDE. We prove that finite particle approximation of Dyson's Brownian motion shows dynamical universality corresponding to geometrical universality. We show this phenomena and construct a general theory of finite particle approximation of ISDE first. Second, we show the density preserving property, that is, Dyson's Brownian motion does not change its density in the time evolution of the process. This property derives strong uniqueness of Dyson's Brownian motion with multiple tails.