A note on the Central Limit Theorem for the Eigenvalue Counting Function of Wigner Matrices

Sandrine Dallaporta, Van Vu

Type: Article

Publication Date: 2011-01-01

Citations: 18

DOI: https://doi.org/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.

Locations

arXiv (Cornell University) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF
Electronic Communications in Probability - View - PDF

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