Lifshitz tails for spectra of Erdős--Rényi random graphs

Details Lifshitz tails for spectra of Erdős--Rényi random graphs Lifshitz tails for spectra of Erdős--Rényi random graphs

2005-02-27

arxiv.org/abs/math-ph/0502054v3

Annals of Applied Probability 2006, Vol. 16, No. 1, 295-309

Physics

Mathematical Physics

Published at http://dx.doi.org/10.1214/1050516000000719 in the Annals of Applied Probability (http://www.imstat.org/aap/) by t

Scientific paper

10.1214/1050516000000719

We consider the discrete Laplace operator $\Delta^{(N)}$ on Erd\H{o}s--R\'{e}nyi random graphs with $N$ vertices and edge probability $p/N$. We are interested in the limiting spectral properties of $\Delta^{(N)}$ as $N\to\infty$ in the subcritical regime $0

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