### Analysis and Probability SeminarLarge-N Segal-Bargmann transform and eigenvalues of random matricesBrian C. Hall (University of Notre Dame)

Monday, April 15, 2019
1:30pm – 2:30pm

Storrs Campus
MONT 313

Abstract: I will describe a generalized Segal-Bargmann transform for compact Lie groups. The transform is a unitary map of Hilbert space of functions on a compact Lie group (for example, the unitary group $$U(N)$$) to a Hilbert space of holomorphic functions on the associated complex group (for example, the general linear group $$GL(N;\mathbb{C})$$). I will then discuss the large-$$N$$ limit of this construction. Finally, I will describe an application of these constructions to random matrix theory: for a certain class of random matrices in $$GL(N;\mathbb{C})$$, the transform allows us to identify the region in the complex plane into which the eigenvalues cluster.

The talk will be self-contained and will include lots of pictures. It is a prequel to the talk I will give at the AMS meeting in Hartford on April 13.

Contact:

Scott Zimmerman, scott.zimmerman@uconn.edu

Analysis and Probability Seminar (primary), UConn Master Calendar