Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random Matrices

Lingyun Li; Matthew Reed; Alexander Soshnikov

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arXiv · 1504.05933

Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random Matrices

Lingyun Li·Matthew Reed·Alexander Soshnikov

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Abstract

We prove the Central Limit Theorem for finite-dimensional vectors of linear eigenvalue statistics of submatrices of Wigner random matrices under the assumption that test functions are sufficiently smooth. We connect the asymptotic covariance to a family of correlated Gaussian Free Fields.

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Lingyun Li, Matthew Reed, Alexander Soshnikov. 2015-04-22. Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random Matrices. https://arxiv.org/abs/1504.05933

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