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Mathematics > Probability

arXiv:1812.10022 (math)
[Submitted on 25 Dec 2018 (v1), last revised 23 Mar 2020 (this version, v3)]

Title:Comparison theorem for some extremal eigenvalue statistics

Authors:Benjamin Landon, Patrick Lopatto, Jake Marcinek
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Abstract: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 Bourgade--Ben Arous 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.
Comments: Revisions
Subjects: Probability (math.PR)
Cite as: arXiv:1812.10022 [math.PR]
  (or arXiv:1812.10022v3 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.10022

Submission history

From: Patrick Lopatto [view email]
[v1] Tue, 25 Dec 2018 04:04:54 UTC (25 KB)
[v2] Wed, 9 Jan 2019 02:38:08 UTC (25 KB)
[v3] Mon, 23 Mar 2020 08:49:56 UTC (30 KB)
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