On the Central Limit Theorem for the Eigenvalue Counting Function of Wigner and Covariance matrices
Probability
2011-02-18 v3
Abstract
This note presents some central limit theorems for the eigenvalue counting function of Wigner matrices in the form of suitable translations of results by Gustavsson and O'Rourke on the limiting behavior of eigenvalues inside the bulk of the semicircle law for Gaussian matrices. The theorems are then extended to large families of Wigner matrices by the Tao and Vu Four Moment Theorem. Similar results are developed for covariance matrices.
Keywords
Cite
@article{arxiv.1011.4042,
title = {On the Central Limit Theorem for the Eigenvalue Counting Function of Wigner and Covariance matrices},
author = {Sandrine Dallaporta},
journal= {arXiv preprint arXiv:1011.4042},
year = {2011}
}
Comments
This paper has been withdrawn because a better result has been achieved and is contained in the following note arXiv:1101.2553, which was written with Van Vu