Open Access
March 2020 Correlated random matrices: Band rigidity and edge universality
Johannes Alt, László Erdős, Torben Krüger, Dominik Schröder
Ann. Probab. 48(2): 963-1001 (March 2020). DOI: 10.1214/19-AOP1379


We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.


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Johannes Alt. László Erdős. Torben Krüger. Dominik Schröder. "Correlated random matrices: Band rigidity and edge universality." Ann. Probab. 48 (2) 963 - 1001, March 2020.


Received: 1 December 2018; Revised: 1 May 2019; Published: March 2020
First available in Project Euclid: 22 April 2020

zbMATH: 07199866
MathSciNet: MR4089499
Digital Object Identifier: 10.1214/19-AOP1379

Primary: 15B52 , 60B20

Keywords: Local law , spectral universality , Tracy–Widom distribution

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 2 • March 2020
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