Modul: MAT971 Stochastische Prozesse

## How much can the eigenvalue of a random matrix fluctuates?

Dr. Gaultier Lambert talk

**Date:** 05.12.18 **Time:** 17.15 - 18.15 **Room:** ETH HG G 43

The goal of this talk is to explain how much the eigenvalues of large Hermitian random matrices deviate from certain deterministic locations. These are known as "rigidity estimates" in the literature and they play a crucial role in the proof of universality. I will review some of the current results on eigenvalues' fluctuations and present a new approach which relies on the theory of Gaussian Multiplicative Chaos and leads to optimal rigidity estimates for the Gaussian Unitary Ensemble. I will also mention how to deduce a central limit theorem from our proof. This is joint work with Tom Claeys, Benjamin Fahs and Christian Webb.