Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs

Abstract

We investigate Laplacians on supercritical bond-percolation graphs with different boundary conditions at cluster borders. The integrated density of states of the Dirichlet Laplacian is found to exhibit a Lifshits tail at the lower spectral edge, while that of the Neumann Laplacian shows a van Hove asymptotics, which results from the percolating cluster. At the upper spectral edge, the behaviour is reversed.

16 pages, typos corrected, to appear in J. Funct. Anal

References in corpus (3)

• Random walks on supercritical percolation clusters
• Spectral properties of the Laplacian on bond-percolation graphs
• Lifshitz tails for spectra of Erdős--Rényi random graphs

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