Work

Mesoscopic spectral CLT for block correlated random matrices

Year: 2025

Type: article

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.

Source: Electronic Journal of Probability

DOI: 10.1214/25-ejp1312

Authors: Torben Krüger, Yuriy Nemish

Institutions: University of Copenhagen, Friedrich-Alexander-Universität Erlangen-Nürnberg, University of California San Diego

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funders: Villum Fonden, Novo Nordisk, Novo Nordisk Fonden