The Marčenko‐Pastur law for sparse random bipartite biregular graphs1. Issue 2 (23rd December 2014) - Dumitriu, Ioana; Johnson, Tobias
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