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2011 A note on the Central Limit Theorem for the Eigenvalue Counting Function of Wigner Matrices
Sandrine Dallaporta, Van Vu
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Electron. Commun. Probab. 16: 214-322 (2011). DOI: 10.1214/ECP.v16-1634

Abstract

The purpose of this note is to establish a Central Limit Theorem for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on the correct asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson, and its extension to large families of Wigner matrices by means of the Tao and Vu Four Moment Theorem and recent localization results by Erd?s, Yau and Yin.

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Sandrine Dallaporta. Van Vu. "A note on the Central Limit Theorem for the Eigenvalue Counting Function of Wigner Matrices." Electron. Commun. Probab. 16 214 - 322, 2011. https://doi.org/10.1214/ECP.v16-1634

Information

Accepted: 22 June 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1226.60009
MathSciNet: MR2819655
Digital Object Identifier: 10.1214/ECP.v16-1634

Subjects:
Primary: 60B20
Secondary: 60F05

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