Date
Tue, 03 May 2022
Time
15:30 - 16:30
Location
Online
Speaker
Fanny Augeri
Organisation
Weizmann Institute of Science

The characteristic polynomial of a random Hermitian matrix induces naturally a field on the real line. In the case of the Gaussian Unitary ensemble (GUE), this fields is expected to have a very special correlation structure: the logarithm of this field is log-correlated and its maximum is at the heart of a conjecture from Fyodorov and Simm predicting its asymptotic behavior.   As a first step in this direction, we obtained in collaboration with R. Butez and O. Zeitouni, a central limit theorem for the logarithm of the characteristic polynomial of the Gaussian beta Ensembles and for a certain class of random Jacobi matrices. In this talk, I will explain how the tridiagonal representation of the GUE and orthogonal polynomials techniques allow us to analyse the fluctuations of the characteristic polynomial.

Last updated on 29 Apr 2022, 3:58pm. Please contact us with feedback and comments about this page.