The Marčenko-Pastur law for sparse random bipartite biregular graphs

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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).