Speaker: Igor Wigman, professor, King’s College London

Date: May 8, 2024

Time: 10:00-11:00

Location: C702, Mingde Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

This talk is based on a joint work with Zeev Rudnick. We study the variance of a linear statistic of the Laplace eigenvalues on a hyperbolic surface, when the surface varies over the moduli space of all surfaces of fixed genus, sampled at random according to the Weil-Petersson measure. The ensemble variance of the linear statistic was recently shown to coincide with that of the corresponding statistic in the Gaussian Orthogonal Ensemble (GOE) of random matrix theory, in the double limit of first taking large genus and then shrinking size of the energy window. We show that in this same limit, the energy variance for a typical surface is close to the GOE result, a feature called“ergodicity”in the random matrix theory literature.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/190642.htm