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.
https://hal-ens-lyon.archives-ouvertes.fr/ensl-01400946
Contributor : Alice Guionnet
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Submitted on : Friday, November 25, 2016 - 3:13:49 PM
Last modification on : Wednesday, June 26, 2019 - 2:48:03 PM
Long-term archiving on : Monday, March 20, 2017 - 4:36:17 PM
A Edelman, Alice Guionnet, S Péché. Beyond universality in random matrix theory. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2016, 26 (3), pp.1659 - 1697. ⟨10.1214/15-AAP1129⟩. ⟨ensl-01400946⟩
