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

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.

References in corpus (5)

• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• High Dimensional Statistical Inference and Random Matrices
• Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
• On fluctuations of eigenvalues of random band matrices
• Mesoscopic linear statistics of Wigner matrices

Cited by in corpus (1)

• The Common Limit of the Linear Statistics of Zeros of Random Polynomials and Their Derivatives