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Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs

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.

preprint2007arXivOpen access
Peter MüllerPeter Stollmann
math-phmath.PRmath.MPmath.SPcond-mat.dis-nn
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Peter MüllerPeter Stollmann

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