Mesoscopic Spectral CLT for Block Correlated Random Matrices
Probability
2023-06-30 v2 Mathematical Physics
Functional Analysis
math.MP
Abstract
For random matrices with block correlation structure we show that the fluctuations of linear eigenvalue statistics are Gaussian on all mesoscopic scales with universal variance which coincides with that of the Gaussian unitary or Gaussian orthogonal ensemble, depending on the symmetry class of the model. The main tool used for determining this variance is a two-point version of the matrix-valued Dyson equation, that encodes the asymptotic behavior of the product of resolvents at different spectral parameters.
Cite
@article{arxiv.2303.17020,
title = {Mesoscopic Spectral CLT for Block Correlated Random Matrices},
author = {Torben Krüger and Yuriy Nemish},
journal= {arXiv preprint arXiv:2303.17020},
year = {2023}
}
Comments
42 pages; typos corrected, references added