The Marčenko-Pastur law for sparse random bipartite biregular graphs

AbstractWe 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