Multiplicative chaos for the characteristic polynomial of the circular β-ensemble

Vortrag von Prof. Dr. Gaultier Lambert

Datum: 29.10.25  Zeit: 17.15 - 18.45  Raum: ETH HG G 43

The circular β-ensemble (CβE)  is a classical model in random
matrix theory which generalizes the eigenvalue process of Haar-
distributed unitary random matrix. It can be interpreted as a system of
two-dimensional point charges at equilibrium on the unit circle.
The goal of this talk is to explain how to describe the asymptotics
properties of the CβE characteristic polynomial using the theory of
orthogonal polynomials on the unit circle (OPUC). I will show that
renormalized powers of the characteristic polynomial converge to
multiplicative chaos measures. If time permits, I will explain the
connection with the eigenvalue counting function, eigenvalue rigidity
and previous results on the CβE spectral measure and the Fyodorov-
Bouchaud conjecture.
This is joint work with Joseph Najnudel (University of Bristol).