The Marčenko‐Pastur law for sparse random bipartite biregular graphs1. Issue 2 (23rd December 2014)

• Record Type: Journal Article
• Authors: Dumitriu, Ioana; Johnson, Tobias
• Is Part Of: Random structures & algorithms. Volume 48:Issue 2(2016)
• Page Start: 313
• Page End: 340
• Publication Date: 2014-12-23
• Subjects: Marčenko‐Pastur law -- random bipartite graphs -- spectral distribution -- Wishart matrix; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20581
• Languages: English
• ISSNs: 1042-9832

Abstract

Abstract: We prove that the empirical spectral distribution of a ( d L, d R )‐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