The Marčenko‐Pastur law for sparse random bipartite biregular graphs |
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| Authors: | Ioana Dumitriu Tobias Johnson |
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| Institution: | 1. Department of Mathematics, University of Washington, Seattle, Washington;2. Department of Mathematics, University of Southern California, Los Angeles, California |
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| Abstract: | We prove that the empirical spectral distribution of a (dL, dR)‐biregular, bipartite random graph, under certain conditions, converges to a symmetrization of the Mar?enko‐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 |
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| Keywords: | Marč enko‐Pastur law random bipartite graphs spectral distribution Wishart matrix |
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