The Marčenko-Pastur law for sparse random bipartite biregular graphs

We prove that the empirical spectral distribution of a (dL, dR)‐biregular, bipartite random graph, under certain conditions, converges to a symmetrization of the Marčenko‐Pastur distribution of random matrix theory. This convergence is not only global (on fixed‐length intervals) but also local (on i...

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Bibliographic Details
Published inRandom structures & algorithms Vol. 48; no. 2; pp. 313 - 340
Main Authors Dumitriu, Ioana, Johnson, Tobias
Format Journal Article
LanguageEnglish
Published Hoboken Blackwell Publishing Ltd 01.03.2016
Wiley Subscription Services, Inc
Subjects
Marčenko-Pastur law
random bipartite graphs
spectral distribution
Wishart matrix
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ISSN1042-9832
1098-2418
DOI10.1002/rsa.20581

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Summary:We prove that the empirical spectral distribution of a (dL, dR)‐biregular, bipartite random graph, under certain conditions, converges to a symmetrization of the Marčenko‐Pastur distribution of random matrix theory. This convergence is not only global (on fixed‐length intervals) but also local (on intervals of increasingly smaller length). Our method parallels the one used previously by Dumitriu and Pal (2012). © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 48, 313–340, 2016
Bibliography:ark:/67375/WNG-VWPSPDX8-L
istex:48EE73A7A5548D019B5BD4F2EB583A7F7AF3E386
Support from NSF CAREER Award (DMS-0847661) (to I.D. and T.J.); NSF (DMS-1401479) (to T.J.).
ArticleID:RSA20581
NSF CAREER - No. DMS-0847661
NSF - No. DMS-1401479
Support from NSF CAREER Award (DMS‐0847661) (to I.D. and T.J.); NSF (DMS‐1401479) (to T.J.).
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ISSN:1042-9832
1098-2418
DOI:10.1002/rsa.20581