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Small deviation estimates for the largest eigenvalue of Wigner matrices (2112.12093v2)
Published 22 Dec 2021 in math.PR, math.ST, and stat.TH
Abstract: We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail.