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June 2016 Beyond universality in random matrix theory
Alan Edelman, A. Guionnet, S. Péché
Ann. Appl. Probab. 26(3): 1659-1697 (June 2016). DOI: 10.1214/15-AAP1129


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.


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Alan Edelman. A. Guionnet. S. Péché. "Beyond universality in random matrix theory." Ann. Appl. Probab. 26 (3) 1659 - 1697, June 2016.


Received: 1 July 2014; Revised: 1 July 2015; Published: June 2016
First available in Project Euclid: 14 June 2016

zbMATH: 06618838
MathSciNet: MR3513602
Digital Object Identifier: 10.1214/15-AAP1129

Primary: 15A52

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.26 • No. 3 • June 2016
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