AUTHOR=Li Lingyun , Reed Matthew , Soshnikov Alexander 

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

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=6

YEAR=2020

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2020.00017

DOI=10.3389/fams.2020.00017

ISSN=2297-4687

ABSTRACT=<p>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.</p>