On the Central Limit Theorem for the Eigenvalue Counting Function of Wigner and Covariance matrices

Details On the Central Limit Theorem for the Eigenvalue Counting Function of Wigner and Covariance matrices On the Central Limit Theorem for the Eigenvalue Counting Function of Wigner and Covariance matrices

2010-11-17

arxiv.org/abs/1011.4042v3

Mathematics

Probability

This paper has been withdrawn because a better result has been achieved and is contained in the following note arXiv:1101.2553

Scientific paper

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.

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