Open Access
February 2006 Lifshitz tails for spectra of Erdős–Rényi random graphs
Oleksiy Khorunzhiy, Werner Kirsch, Peter Müller
Ann. Appl. Probab. 16(1): 295-309 (February 2006). DOI: 10.1214/1050516000000719
Abstract

We consider the discrete Laplace operator Δ(N) on Erdős–Rényi random graphs with N vertices and edge probability p/N. We are interested in the limiting spectral properties of Δ(N) as N→∞ in the subcritical regime 0<p<1 where no giant cluster emerges. We prove that in this limit the expectation value of the integrated density of states of Δ(N) exhibits a Lifshitz-tail behavior at the lower spectral edge E=0.

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Copyright © 2006 Institute of Mathematical Statistics
Oleksiy Khorunzhiy, Werner Kirsch, and Peter Müller "Lifshitz tails for spectra of Erdős–Rényi random graphs," The Annals of Applied Probability 16(1), 295-309, (February 2006). https://doi.org/10.1214/1050516000000719
Published: February 2006
Vol.16 • No. 1 • February 2006
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