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Central Limit Theorem for Linear Statistics of Eigenvalues of Band Random Matrices · arXivDesk

1304.6744Apr 24, 2013minor revision; to appear in Random Matrices: Theory and Applications

Central Limit Theorem for Linear Statistics of Eigenvalues of Band Random Matrices

Lingyun Li, Alexander Soshnikov

Abstract

We prove the Central Limit Theorem for linear statistics of the eigenvalues of band random matrices provided $\sqrt{n} \ll b_n \ll n$

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We prove the Central Limit Theorem for linear statistics of the eigenvalues of band random matrices provided √n ≪ b_n ≪ n and test functions are sufficiently smooth.

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Claims

The paper addresses: Central Limit Theorem for Linear Statistics of Eigenvalues of Band Random Matrices.
We prove the Central Limit Theorem for linear statistics of the eigenvalues of band random matrices provided √n ≪ b_n ≪ n and test functions are sufficiently smooth.

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Author comment: minor revision; to appear in Random Matrices: Theory and Applications