Journal
ANNALS OF APPLIED PROBABILITY
Volume 16, Issue 1, Pages 295-309Publisher
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/1050516000000719
Keywords
random graphs; spectra of graphs; Laplace operator; eigenvalue distribution
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We consider the discrete Laplace operator Delta((N)) on Erdos-Renyi random graphs with N vertices and edge probability p/N. We are interested in the limiting spectral properties of Delta((N)) as N -> infinity 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 A (N) exhibits a Lifshitz-tail behavior at the lower spectral edge E = 0.
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