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Beyond universality in random matrix theory

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jun 2016Embargo end date: 01 Jan 2014 France, United States, France, France Publisher:Institute of Mathematical StatisticsJournal:The Annals of Applied Probability, volume 26 (issn: 1050-5164,

Copyright policy )Funded by:NSF | Collaborative Research: T..., NSF | Applied Free Probability ..., NSF | Random matrices, free pro... +1 projects

Authors: Edelman, A; Guionnet, Alice; Péché, S;

doi: 10.1214/15-aap1129 , 10.48550/arxiv.1405.7590

arXiv: http://arxiv.org/abs/1405.7590

handle: 1721.1/115297

Beyond universality in random matrix theory

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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)

Countries

France, United States, France, France

Related Organizations

Sorbonne University
France
Massachusetts Institute of Technology
United States
Ecole Normale Supérieure de Lyon
France
University of Paris
France
Massachusetts Institute of Technology
United States

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Keywords

[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], hard edge, Probability (math.PR), singular value, 15A52, Random matrix, FOS: Mathematics, universality, bulk, Wigner matrix, Mathematics - Probability

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