Small deviation estimates for the largest eigenvalue of Wigner matrices

Erdös, László; Xu, Yuanyuan

Small deviation estimates for the largest eigenvalue of Wigner matrices

Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079.

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https://arxiv.org/abs/2112.12093 [Preprint]

DOI

10.3150/22-BEJ1490

Journal Article | Published | English

Scopus indexed

Author

Erdös, László^ISTA ; Xu, Yuanyuan^ISTA

Corresponding author has ISTA affiliation

Department

Erdoes Group

Grant

Random matrices beyond Wigner-Dyson-Mehta

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.

Publishing Year

2023

Date Published

2023-05-01

Journal Title

Bernoulli

Publisher

Bernoulli Society for Mathematical Statistics and Probability

Volume

Issue

Page

1063-1079

ISSN

1350-7265

IST-REx-ID

12707

Cite this

Erdös L, Xu Y. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 2023;29(2):1063-1079. doi:10.3150/22-BEJ1490

Erdös, L., & Xu, Y. (2023). Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. Bernoulli Society for Mathematical Statistics and Probability. https://doi.org/10.3150/22-BEJ1490

Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” Bernoulli. Bernoulli Society for Mathematical Statistics and Probability, 2023. https://doi.org/10.3150/22-BEJ1490.

L. Erdös and Y. Xu, “Small deviation estimates for the largest eigenvalue of Wigner matrices,” Bernoulli, vol. 29, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1063–1079, 2023.

Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079.

Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” Bernoulli, vol. 29, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2023, pp. 1063–79, doi:10.3150/22-BEJ1490.

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