# Student Probability Seminar

#### Large deviations for extreme eigenvalues of deformed Wigner random matrices

Speaker: Benjamin McKenna, CIMS

Location: Warren Weaver Hall 201

Date: Thursday, October 3, 2019, 12:15 p.m.

Synopsis:

Given the spectrum of two $N \times N$ matrices $A$ and $B$, what can we say about the spectrum of $A+B$ as $N \to \infty$? In this talk, we will discuss a random analogue of this deterministic question. We will introduce the free additive convolution, which gives an asymptotic understanding of the whole spectrum; present a large deviations principle, which gives a fine understanding at the edge of the spectrum; and consider "spherical integrals," which are the major tool in the proof of the latter. No previous knowledge of random matrices will be assumed.