Graduate Student Seminar: Optimal bounds on the largest eigenvalue of inhomogeneous random matrices Speaker: Tatiana Brailovskaya

In this talk, I will discuss sharp non-asymptotic bounds on the expectation of the largest eigenvalue of a Gaussian random matrix with independent entries and arbitrary variance structure. Bounds of this kind are of significant interest to applied mathematicians and computer scientists, however classical random matrix theory fails to capture the behavior of such objects. Our methods build upon prior work on this subject by Bandeira & Van Handel (2016) and allow us to improve their results by replacing universal constants with optimal numerical values. This talk will be accessible to anyone with basic probability and linear algebra background.

(This is a joint research project with Prof. Ramon van Handel)