Maurice Duits: Central Limit Theorems for Orthogonal Polynomial Ensembles

In this talk I will present some recent joint work with Jonathan Breuer on Central Limit Theorems for Orthogonal Polynomial Ensembles, which form an important class of point processes in random matrix theory. An Orthogonal Polynomial Ensemble consists of a probability measure on configurations of points, constructed out of the Christoffel-Darboux kernel corresponding to the orthogonal polynomials. When the number of points in the configuration grows large, the system typically tends to a deterministic limit. I will discuss how the fluctuations around this limit can be effectively described by Central Limit Theorems for linear statistics. The main goal of the talk is to show how the Jacobi operator corresponding to the orthogonal polynomials can be used to obtain a (unexpectedly) general Central Limit Theorem.