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Comparison theorem for some extremal eigenvalue statistics

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arxiv 1812.10022 v3 pith:WDJEQUTV submitted 2018-12-25 math.PR

Benjamin Landon , Patrick Lopatto , Jake Marcinek This is my paper · ORCID
classification math.PR
keywords eigenvaluebulkcomparisonextremalgeneralizedmatricesmaximalsome
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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.

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