Lifshitz Tails for Spectra of Erdős–rényi Random Graphs
نویسنده
چکیده
We consider the discrete Laplace operator ∆ on Erdős–Rényi random graphs with N vertices and edge probability p/N . We are interested in the limiting spectral properties of ∆ 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 ∆ exhibits a Lifshitz-tail behavior at the lower spectral edge E = 0.
منابع مشابه
Lifshits Tails for Spectra of Erdős-rényi Random Graphs by Oleksiy Khorunzhiy
We consider the discrete Laplace operator ∆ on Erdős–Rényi random graphs with N vertices and edge probability p/N . We are interested in the limiting spectral properties of ∆ 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 ∆ exhibits a Lifshits-tail behaviour at the lower spectr...
متن کاملLifshits Tails for Spectra of Erdős-rényi Random Graphs
We consider the discrete Laplace operator ∆ on Erdős–Rényi random graphs with N vertices and edge probability p/N . We are interested in the limiting spectral properties of ∆ 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 ∆ exhibits a Lifshits-tail behaviour at the lower spectr...
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