Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random Matrices - Li, Lingyun; Reed, Matthew; Soshnikov, Alexander (Frontiers in Applied Mathematics and Statistics, 2020)
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.