## Speaker:

Lucas Benigni

## Speaker Link:

## Institution:

University of Chicago

## Time:

Wednesday, May 11, 2022 - 2:00pm to 3:00pm

## Host:

## Location:

510R Rowland Hall

We prove a strong form of delocalization of eigenvectors for general large random matrices called Quantum Unique Ergodicity. These estimates state that the mass of an eigenvector over a subset of entries tends to the uniform distribution. We are also able to prove that the fluctuations around the uniform distribution are Gaussian for a regime of a subset of entries. The proof relies on new eigenvector observables studied dynamically through the Dyson Brownian motion combined with a novel bootstrap comparison argument.