Small deviation estimates for the largest eigenvalue of Wigner matrices
Probability
2022-04-04 v2 Statistics Theory
Statistics Theory
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.
Keywords
Cite
@article{arxiv.2112.12093,
title = {Small deviation estimates for the largest eigenvalue of Wigner matrices},
author = {László Erdős and Yuanyuan Xu},
journal= {arXiv preprint arXiv:2112.12093},
year = {2022}
}
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