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

04/22/2015

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by   Lingyun Li, et al.

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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.