Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs
Mathematical Physics
2011-11-10 v2 Disordered Systems and Neural Networks
math.MP
Probability
Spectral Theory
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.
Keywords
Cite
@article{arxiv.math-ph/0506053,
title = {Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs},
author = {Peter Müller and Peter Stollmann},
journal= {arXiv preprint arXiv:math-ph/0506053},
year = {2011}
}
Comments
16 pages, typos corrected, to appear in J. Funct. Anal