Eigenvalues of Random Matrices in the General Linear Group in the Large-$N$ Limit

Abstract

I will consider random matrices in the general linear group GL(N;C) distributed according to a heat kernel measure. This may also be described as the distribution of Brownian motion in GL(N;C) starting at the identity. Numerically, the eigenvalues appear to cluster into a certain domain Σt as N tends to infinity. A natural candidate for the limiting eigenvalue distribution is the Brown measure of the limiting object, which is Bianes “free multiplicative Brownian motion.” I will describe recent work with Driver and Kemp in which we compute this Brown measure. The talk will be self contained and will have lots of pictures. Host: Todd Kemp Tuesday, February 5, 2019 11:00 AM AP&M 6402 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *