Douglas Lectures

Date: November 15, 2016

Time: 4:00PM - 5:00PM

Location: BLOCKER 117

Speaker: Hari Bercovici, Indiana University

Title: Eigenvalues of sums of matrices: Random Matrices

Abstract: The eigenvalues of a sum of random selfadjoint matrices can be described quite accurately in terms of the summands. For instance, suppose that P and Q are two matrices of size N, chosen randomly and independently among the orthogonal projections of rank [N/2]. For large N, the eigenvalues of the sum P+Q approximate very accurately an arcsine distribution on the interval [0,2]. This is explained by free probability and by the concentration of measure phenomenon. Interestingly, one can even predict where the stray eigenvalues of the sum tend to appear. This is also explained by free probability.