Lifshitz tails for spectra of Erdos-Renyi random graphs

• 成果类型: Article
• 署名作者: Khorunzhiy, O; Kirsch, W; Müller, P
• 署名单位: Universite Paris Saclay; University of Gottingen; Ruhr University Bochum; Ruhr University Bochum
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/1050516000000719
• 发表日期: 2006
• 页码: 295-309
• 关键词: sparse random matrices; eigenvalue distribution; energy spectrum; density; STATES; approximation; MODEL

摘要

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.