Rostyslav Kozhan: Random unitary and subunitary matrices via orthogonal polynomials and CMV matrices

Abstract: We compute explicitly the joint law of eigenvalues of truncations (i.e., with one row and column removed) of unitary and orthogonal ensembles of random matrices. This includes the truncations of Dyson's circular ensembles CUE, COE, and CSE, as well as of the orthogonal group. The main tool is to reduce the problem to studying zeros of orthogonal polynomials on the unit circle. We also show that the point process of these eigenvalues appears as a universal limit of density of states of CMV matrices with decaying random coefficients.

This is joint work with Rowan Killip (UCLA).