# CENTRAL LIMIT THEOREM FOR LINEAR EIGENVALUE STATISTICS OF RANDOM MATRICES WITH INDEPENDENT ENTRIES

```@article{Lytova2009CENTRALLT,
title={CENTRAL LIMIT THEOREM FOR LINEAR EIGENVALUE STATISTICS OF RANDOM MATRICES WITH INDEPENDENT ENTRIES},
author={Anna Lytova and Leonid A. Pastur},
journal={Annals of Probability},
year={2009},
volume={37},
pages={1778-1840}
}```
• Published 26 September 2008
• Mathematics
• Annals of Probability
We consider n x n real symmetric and Hermitian Wigner random matrices n ―1/2 W with independent (modulo symmetry condition) entries and the (null) sample covariance matrices n ―1 X*X with independent entries of m x n matrix X. Assuming first that the 4th cumulant (excess) κ 4 of entries of W and X is zero and that their 4th moments satisfy a Lindeberg type condition, we prove that linear statistics of eigenvalues of the above matrices satisfy the central limit theorem (CLT) as n → ∞, m → ∞, m/n…
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