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Probability and Computational Finance Seminar
Todd Kemp
University of California San Diego
Title: Random Matrices, Brownian Motion, and Lie Groups

Abstract: Random matrix theory studies the behavior of the eigenvalues (or singular values) of random matrices as the dimension grows. Initiated by Wigner in the 1950s, there is now a rich and well-developed theory of the universal behavior of such random eigenvalues in models that are natural generalizations of the Gaussian case.

In this talk, I will discuss a generalization of these kinds of results in a new direction. A Gaussian random matrix can be thought of as an instance of Brownian motion on a Lie algebra; this opens the door to studying the eigenvalues (and singular values) of Brownian motion on Lie groups. I will present recent progress understanding the asymptotic spectral distribution of Brownian motion on unitary groups and general linear groups.

Date: Monday, April 27, 2015
Time: 4:30 pm
Location: Wean Hall 6423
Submitted by:  Solesne Bourguin