Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs

Details Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs

2005-06-21

arxiv.org/abs/math-ph/0506053v2

J. Funct. Anal. 252, 233-246 (2007)

Physics

Mathematical Physics

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

Scientific paper

10.1016/j.jfa.2007.06.018

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.

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