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arXiv · 1304.4907

The Mar\v{c}enko-Pastur law for sparse random bipartite biregular graphs

Ioana Dumitriu·Tobias Johnson
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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 Mar\v{c}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).

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Ioana Dumitriu, Tobias Johnson. 2013-04-17. The Mar\v{c}enko-Pastur law for sparse random bipartite biregular graphs. https://doi.org/10.1002/rsa.20581

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