The Marčenko-Pastur law for sparse random bipartite biregular graphs
arXiv:1304.4907 · doi:10.1002/rsa.20581
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).
29 pages; minor changes in response to referees' comments
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