Abstract:

Integrable ensembles of random matrix theory can be divided into three symmetry types: unitary, orthogonal, and symplectic. The first symmetry type leads to determinantal point processes, the ensembles of orthogonal and symplectic symmetry types define the Pfaffian point processes.

The aim of my talk is to describe determinantal and Pfaffian point processes of random matrix type arising in the the harmonic analysis on the infinite symmetric group.

The talk is self-contained, and should be suitable for graduate students.