Webinar: Gaultier Lambert (KTH) September 27

We are happy to announce the that the first webinar of the fall 2024 will be given by Gaultier Lambert (KTH).

When: Friday September 27, 11.00-11.45

Where: Zoom: https://kth-se.zoom.us/j/63335108409

Title: On the circular unitary ensemble

Abstract: The goal of the talk is to give an introduction to random matrix theory using the simplest model known as the circular unitary ensemble (CUE). This model, introduced by Dyson, considers the eigenvalues of a random matrix from the unitary group sampled according to the Haar measure. I will review a few of the basic results on the CUE, including how to sample from the Haar measure, the joint distribution of the eigenvalues and its consequences, the Gaussian fluctuations of the eigenvalues and the sine process. Several of these results are universal for the eigenvalues of Hermitian random matrix and I will try to convey that there are easy to prove for the CUE. I will also mention some important connections with analysis, in particular to the statistics of zeros of the Riemann zeta function and the asymptotics of Toeplitz determinants.