Beyond universality in random matrix theory

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.

Published at http://dx.doi.org/10.1214/15-AAP1129 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Gaussian fluctuations for linear spectral statistics of large random covariance matrices
• Functional CLT for sample covariance matrices
• A note on the expansion of the smallest eigenvalue distribution of the LUE at the hard edge

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