Electronic Journal of Probability

Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails

Fanny Augeri

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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.

Article information

Source
Electron. J. Probab., Volume 21 (2016), paper no. 32, 49 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1461007173

Digital Object Identifier
doi:10.1214/16-EJP4146

Mathematical Reviews number (MathSciNet)
MR3492936

Zentralblatt MATH identifier
1338.60010

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 60F10: Large deviations

Keywords
random matrices large deviations

Rights
Creative Commons Attribution 4.0 International License.

Citation

Augeri, Fanny. Large deviations principle for the largest eigenvalue of Wigner matrices without Gaussian tails. Electron. J. Probab. 21 (2016), paper no. 32, 49 pp. doi:10.1214/16-EJP4146. https://projecteuclid.org/euclid.ejp/1461007173


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