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

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arxiv 1304.6744 v4 pith:Z6N5WKT5 submitted 2013-04-24 math.PR math-phmath.MP

Lingyun Li , Alexander Soshnikov This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords bandcentraleigenvalueslimitlinearmatricesrandomstatistics
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abstract

We prove the Central Limit Theorem for linear statistics of the eigenvalues of band random matrices provided $\sqrt{n} \ll b_n \ll n$ and test functions are sufficiently smooth.

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  1. Some estimates for generalized Wigner matrix linear spectral statistics

    math.PR 2024-12 conditional novelty 8.0 of 10

    For generalized Wigner matrices, the characteristic function of linear spectral statistics is expanded around its Gaussian limit with error O(N^{-1}) and an explicit N^{-1/2} correction.

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