EVENT DETAILS AND ABSTRACT

Title: Extremal and critical eigenvalue statistics of random matrices
Speaker: Benjamin Landon
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

We discuss recent results on classes of random eigenvalue statistics of critical or extremal nature. The study of the largest gap between consecutive eigenvalues of random matrices was first urged by Diaconis with the goal of understanding the correspondence between random matrices and number theory. We present a comparison theorem that shows that this quantity is universal within the class of generalized Wigner matrices. The fluctuations of a single bulk eigenvalue and the eigenvalue counting function were determined by Gustavsson for the GUE. We discuss the universality of these quantities for general classes of matrices, and lower order corrections showing that these quantities are essentially on the boundary between universal and non-universal fluctuations.

Joint work with P. Lopatto, J. Marcinek and P. Sosoe