Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs
arXiv:math-ph/0506053 · doi:10.1016/j.jfa.2007.06.018
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