On the spectral distribution of large weighted random regular graphs

@article{Goldmakher2013OnTS,
  title={On the spectral distribution of large weighted random regular graphs},
  author={Leo Goldmakher and Cap Khoury and Steven J. Miller and Kesinee Ninsuwan},
  journal={arXiv: Probability},
  year={2013}
}
McKay proved that the limiting spectral measures of the ensembles of $d$-regular graphs with $N$ vertices converge to Kesten's measure as $N\to\infty$. In this paper we explore the case of weighted graphs. More precisely, given a large $d$-regular graph we assign random weights, drawn from some distribution $\mathcal{W}$, to its edges. We study the relationship between $\mathcal{W}$ and the associated limiting spectral distribution obtained by averaging over the weighted graphs. Among other… 
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