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.
Publié le : 2005-06-20
Classification:
Mathematical Physics,
Condensed Matter - Disordered Systems and Neural Networks,
Mathematics - Probability,
Mathematics - Spectral Theory,
47B80,
34B45, 05C80
@article{0506053,
author = {M\"uller, Peter and Stollmann, Peter},
title = {Spectral asymptotics of the Laplacian on supercritical bond-percolation
graphs},
journal = {arXiv},
volume = {2005},
number = {0},
year = {2005},
language = {en},
url = {http://dml.mathdoc.fr/item/0506053}
}
Müller, Peter; Stollmann, Peter. Spectral asymptotics of the Laplacian on supercritical bond-percolation
graphs. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0506053/