Eugene Strahov (Hebrew University)

Title:  Determinantal processes related to products of random matrices.

Abstract:

I will discuss a family of random processes in discrete time related to products of random matrices (product matrix processes). Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product plays a role of a discrete time. I will explain that in certain cases product matrix processes are discrete-time determinantal point processes, whose correlation kernels can be expressed in terms of double contour integrals. This enables to investigate determinantal processes for products of random matrices in different asymptotic regimes, and to compute different probabilistic quantities of interest.