The Mar\v{c}enko-Pastur law for sparse random bipartite biregular graphs
Probability
2016-01-22 v2 Combinatorics
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).
Keywords
Cite
@article{arxiv.1304.4907,
title = {The Mar\v{c}enko-Pastur law for sparse random bipartite biregular graphs},
author = {Ioana Dumitriu and Tobias Johnson},
journal= {arXiv preprint arXiv:1304.4907},
year = {2016}
}
Comments
29 pages; minor changes in response to referees' comments