Analysis Seminar-Local limits of Dyson's Brownian Motion at multiple times.

Speaker:   Professor Diane Holcomb, University of Arizona. (Diane graduated from GW in 2008, got a PhD from Wisconsin, and is now a postdoc at Arizona.)

Date: Tuesday, April 5 at 1:00 PM

Where: Rome 351

Title:  Local limits of Dyson's Brownian Motion at multiple times. 

Abstract:  Dyson's Brownian Motion may be thought of as a generalization of  Brownian Motion to the matrix setting. We can study the eigenvalues of a Dyson's Brownian motion at multiple times. The resulting object has different "color" points corresponding to the eigenvalues at different times. Similar to a single time, the correlation functions of the process may be described in terms of determinantal formulas. We study the local behavior of the eigenvalues as we take the dimension of the associated matrix to infinity. The resulting limiting process in the bulk is again determinantal and is described with an "extended sine kernel." This work aims to give an alternate description of the limiting process in terms of the counting function. In this seminar I will go over the the description and methods for finding such a limit. This is work in progress and is joint with Elliot Paquette (Weizmann Institute).