Author(s):

Bourgade, Paul; Erdős, László; Yau, Horngtzer; Yin, Jun

Article Title: 
Fixed energy universality for generalized wigner matrices

Affiliation 
IST Austria 
Abstract: 
We prove the WignerDysonMehta 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.

Journal Title:

Communications on Pure and Applied Mathematics

Volume: 
69

Issue 
10

ISSN:

10970312

Publisher:

WileyBlackwell

Date Published:

20161001

Start Page: 
1815

End Page:

1881

URL: 

DOI: 
10.1002/cpa.21624

Notes: 
The work of P.B. was partially supported by National Sci
ence Foundation Grant DMS1208859. The work of L.E. was partially supported
by ERC Advanced Grant RANMAT 338804. The work of H.T. Y. was partially
supported by National Science Foundation Grant DMS1307444 and a Simons In
vestigator award. The work of J.Y. was partially supported by National Science
Foundation Grant DMS1207961. The major part of this research was conducted
when all authors were visiting IAS and were also supported by National Science
Foundation Grant DMS1128255.

Open access: 
yes (repository) 