Work

Beyond universality in random matrix theory

Year: 2016

Type: article

Abstract: In order to have a better understanding of finite random matrices with non-Gaussian entries, we study the $1/N$ expansion of local eigenvalue statistics in both the bulk and at the hard edge of the spectrum of random matrices. This gives valuable information about the smallest singular value not seen in universality laws. In particular, we show the dependence on the fourth moment (or the kurtosis) of the entries. This work makes use of the so-called complex Gaussian divisible ensembles for both Wigner and sample covariance matrices.

Source: The Annals of Applied Probability

DOI: 10.1214/15-aap1129

Authors: Alan Edelman, A. Guionnet, S. Péché

Institutions: Massachusetts Institute of Technology, Unité de Mathématiques Pures et Appliquées, Laboratoire de Probabilités et Modèles Aléatoires, Université Paris Diderot

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Simons Foundation

OpenAlex ID: W2096545511