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2016 Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails
Fanny Augeri
Electron. J. Probab. 21(none): 1-49 (2016). DOI: 10.1214/16-EJP4146

Abstract

We prove a large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails, that is, the distribution tails of the diagonal entries $\mathbb{P} ( |X_{1,1}|>t)$ and off-diagonal entries $\mathbb{P} (|X_{1,2}|>t)$ behave like $e^{-bt^{\alpha }}$ and $e^{-at^{\alpha }}$ respectively, for some $a,b\in (0,+\infty )$ and $\alpha \in (0,2)$. The large deviations principle is of speed $N^{\alpha /2}$, and with a good rate function depending only on the distribution tail of the entries.

Citation

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Fanny Augeri. "Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails." Electron. J. Probab. 21 1 - 49, 2016. https://doi.org/10.1214/16-EJP4146

Information

Received: 27 February 2015; Accepted: 27 January 2016; Published: 2016
First available in Project Euclid: 18 April 2016

zbMATH: 1338.60010
MathSciNet: MR3492936
Digital Object Identifier: 10.1214/16-EJP4146

Subjects:
Primary: 60B20, 60F10

JOURNAL ARTICLE
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Vol.21 • 2016
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