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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