Beyond universality in random matrix theory
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1405.7590.pdf
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Author(s)
Péché, S.
Edelman, Alan
Guionnet, Alice
Date Issued
June 2016
Journal
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1214/15-AAP1129
