Title: Perturbations of Random Matrices
Speaker: Philip Matchett Wood (University of Wisconsin at Madison)
Abstract: For many models of n by n random matrices, the distribution of eigenvalues approaches a fixed limit distribution as the size n goes to infinity. This phenomenon follows the general idea that aggregating lots of independent sources of randomness often results in a non-random object; for example, this is one way of thinking of the central limit theorem. This talk will explore what happens to the eigenvalue distribution when the random matrix is perturbed by adding a fixed n by n matrix. The talk will describe a new result on perturbations that do not change the bulk eigenvalue distribution but do cause some isolated eigenvalues to appear---so called "outlier eigenvalues"---and the talk will also discuss a new result that quantifies changes in the limiting eigenvalue distribution when a random Hermitian matrix is perturbed by a non-Hermitian matrix. The talk will include joint work with Sean O'Rourke and joint work with Alice Guionnet and Ofer Zeitouni.
