Open Access
November 2020 Comparison theorem for some extremal eigenvalue statistics
Benjamin Landon, Patrick Lopatto, Jake Marcinek
Ann. Probab. 48(6): 2894-2919 (November 2020). DOI: 10.1214/20-AOP1439


We introduce a method for the comparison of some extremal eigenvalue statistics of random matrices. For example, it allows one to compare the maximal eigenvalue gap in the bulk of two generalized Wigner ensembles, provided that the first four moments of their matrix entries match. As an application, we extend results of Ben Arous–Bourgade and Feng–Wei that identify the limit of the maximal eigenvalue gap in the bulk of the GUE to all complex Hermitian generalized Wigner matrices.


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Benjamin Landon. Patrick Lopatto. Jake Marcinek. "Comparison theorem for some extremal eigenvalue statistics." Ann. Probab. 48 (6) 2894 - 2919, November 2020.


Received: 1 December 2018; Revised: 1 March 2020; Published: November 2020
First available in Project Euclid: 20 October 2020

MathSciNet: MR4164456
Digital Object Identifier: 10.1214/20-AOP1439

Primary: 60B20

Keywords: Dyson Brownian motion , Eigenvalues , Extreme value theory , Random matrix theory , Universality

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 6 • November 2020
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