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.
Citation
László Erdős. Yuanyuan Xu. "Small deviation estimates for the largest eigenvalue of Wigner matrices." Bernoulli 29 (2) 1063 - 1079, May 2023. https://doi.org/10.3150/22-BEJ1490
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