Home /  Workshop /  Schedules /  Fluctuations of the Characteristic Polynomial of Random Jacobi Matrices

Fluctuations of the Characteristic Polynomial of Random Jacobi Matrices

[HYBRID WORKSHOP] Connections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 2 September 20, 2021 - September 24, 2021

September 20, 2021 (10:35 AM PDT - 11:25 AM PDT)
Speaker(s): Fanny Augeri (Weizmann Institute of Science)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video
No Video Uploaded
Abstract

The characteristic polynomial of the GUE is at the heart of a conjecture from Fyodorov and Simm, where it is crucial to understand the log-correlated structure of the field induced. As a first step in this direction, we obtain a central limit theorem for the logarithm of the characteristic polynomial of the Gaussian $\beta$ Ensemble. Relying on the tridiagonal representation of such matrix models, we will explain how the second order recursion satisfied by the characteristic polynomial allows us to give a martingale representation of its logarithm, leading to an analysis of its fluctuations. This is a joint work with R. Butez and O. Zeitouni.

Supplements
91605?type=thumb Fluctuations of the Characteristic Polynomial of Random Jacobi Matrices 731 KB application/pdf Download
Video/Audio Files
No Video Files Uploaded