Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random
- Author(s): Li, Lingyun;
- Reed, Matthew;
- Soshnikov, Alexander
- et al.
Published Web Locationhttps://arxiv.org/pdf/1504.05933.pdf
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.