Student Probability Seminar

The characteristic polynomial of a random unitary matrix: a probabilistic approach

Speaker: Krishnan Mody, CIMS

Location: Warren Weaver Hall 1314

Date: Monday, March 9, 2020, 11:45 a.m.

Synopsis:

The Circular Unitary Ensemble is a classical random matrix ensemble which has been well studied in recent years due to its heuristic connection to the Riemann zeta function. In this talk, I will present a central limit theorem for the log-characteristic polynomial of CUE distributed matrices in the limit of large dimension. The result goes back to Keating and Snaith, but I will present a proof due to Bourgade, Hughes, Nikeghbali, and Yor. This CLT resembles a CLT for the log of the zeta function on the critical axis, due to Selberg.