Infinite-dimensional SDE related to random matrices — finite particle approximation and the density preserving property by Yosuke Kawamoto

Event Date: 

Wednesday, February 24, 2016 -
3:30pm to 5:00pm

Event Date Details: 

Refreshments served at 3:15 p.m.

Event Location: 

  • South Hall 5607F

Yosuke Kawamoto — Kyushu University 

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.