2000 character limit reached
Fixed energy universality for generalized Wigner matrices (1407.5606v3)
Published 21 Jul 2014 in math.PR, math-ph, and math.MP
Abstract: We prove the Wigner-Dyson-Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random matrices either require an averaging in the energy parameter or they hold only for Hermitian matrices if the energy parameter is fixed. We develop a homogenization theory of the Dyson Brownian motion and show that microscopic universality follows from mesoscopic statistics.
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.