Beyond universality in random matrix theory
Author(s)
Péché, S.; Edelman, Alan; Guionnet, Alice
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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.
Date issued
2016-06Department
Massachusetts Institute of Technology. Department of MathematicsJournal
The Annals of Applied Probability
Publisher
Institute of Mathematical Statistics
Citation
Edelman, Alan et al. “Beyond Universality in Random Matrix Theory.” The Annals of Applied Probability 26, 3 (June 2016): 1659–1697 © 2016 Institute of Mathematical Statistics
Version: Author's final manuscript
ISSN
1050-5164