Universality for a class of random band matrices

Abstract

We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, $W\sim N$. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.

References in corpus (1)

• Quadratic vector equations on complex upper half-plane

Cited by in corpus (5)

• Some Open Problems in Random Matrix Theory and the Theory of Integrable Systems. II
• Characteristic polynomials for 1D random band matrices from the localization side
• Universality of random matrices with correlated entries
• Local spectral statistics of the addition of random matrices
• Universality of the least singular value for the sum of random matrices