Workshop: Solvable families of random block tridiagonals

Speaker
Brian Rider, Temple University

Abstract
The tridiagonal matrix models for the Gaussian beta-ensembles of Dumitriu-Edelman have been the launching point for a huge number of results over the last many years. Here we explore their original approach in the block setting, and obtain two families of random tridiagonal block models for which the joint eigenvalue distribution can be computed explicitly. The “random operator approach” then allows us to establish point process limits of the corresponding eigenvalues at the edge(s). Along the way, we discover certain algebraic identities involving Vandermonde determinants which could be of independent interest. Joint work with Benedek Valkó.