Small deviation estimates for the largest eigenvalue of Wigner matrices

László Erdős; Yuanyuan Xu

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arXiv · 2112.12093

Small deviation estimates for the largest eigenvalue of Wigner matrices

László Erdős·Yuanyuan Xu

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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.

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László Erdős, Yuanyuan Xu. 2021-12-22. Small deviation estimates for the largest eigenvalue of Wigner matrices. https://arxiv.org/abs/2112.12093

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