Student Probability Seminar

The Characteristic Polynomial of a Random Unitary Matrix

Speaker: Guillaume Dubach

Location: Warren Weaver Hall 1314

Date: Tuesday, October 25, 2016, 2 p.m.


We will introduce the Circular Unitary Ensemble (CUE) of random unitary matrices distributed according to the Haar measure on Un(C), and compute the distribution of its characteristic polynomial thanks to an explicit decomposition of the ensemble. In particular, the moments of this characteristic polynomial can be computed ; they are strongly believed to have a link with the moments of the zeta function along its critical line, and we will give some intuitive (but striking) reasons to think it might be true.