Speaker: Ofer Zeitouni, Weizmann Institute
January 5, 2024 02:30 PM
- 03:30 PM
Abstract:
Consider the logarithm of the characteristic polynomial of random matrices from the GOE or GUE, properly centered. We compute the leading order of its asymptotics, and show it is universal in the class of Wigner matrices. In the case of Gaussian divisible entries, the universality extends to a tightness statement. The proof uses in an essential way coupling via stochastic dynamics, and leads to optimal rigidity statements for the eigenvalue at the microscopic level. Joint work with Paul Bourgade and Patrick Lopatto.