# Tim Wuerfel: Expectation values of characteristic polynomials in polynomial ensembles

**Time: **
Tue 2019-11-05 15.15 - 16.15

**Location: **
KTH, Room F11

**Lecturer: **
Tim Wuerfel, Universität Bielefeld

### Abstract

Expectation values of characteristic polynomials are well studied in random matrix ensembles with joint probability density function proportional to the square of the Vandermonde determinant. These ensembles form determinantal point processes and the correlation functions can be obtained via the correlation kernel.

We study more general ensembles, which yield a special biorthogonal structure introduced first by A. Borodin. To compute correlation functions in this setting we need formulas which include expectation values of ratios of characteristic polynomials. Therefore, we derive an integral representation for an arbitrary ratio of characteristic polynomials in so-called polynomial ensembles.