Fixed energy universality for generalized wigner matrices Journal Article


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 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.
Journal Title: Communications on Pure and Applied Mathematics
Volume: 69
Issue 10
ISSN: 1097-0312
Publisher: Wiley-Blackwell  
Date Published: 2016-10-01
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 DMS-1208859. 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 DMS-1307444 and a Simons In- vestigator award. The work of J.Y. was partially supported by National Science Foundation Grant DMS-1207961. The major part of this research was conducted when all authors were visiting IAS and were also supported by National Science Foundation Grant DMS-1128255.
Open access: yes (repository)
IST Austria Authors
  1. László Erdős
    105 Erdős
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