Exact clesed form of the return probability on the Bethe lattice
Condensed Matter
2009-10-22 v1
Abstract
An exact closed form solution for the return probability of a random walk on the Bethe lattice is given. The long-time asymptotic form confirms a previously known expression. It is however shown that this exact result reduces to the proper expression when the Bethe lattice degenerates on a line, unlike the asymptotic result which is singular. This is shown to be an artefact of the asymptotic expansion. The density of states is also calculated.
Cite
@article{arxiv.cond-mat/9411113,
title = {Exact clesed form of the return probability on the Bethe lattice},
author = {Achille Giacometti},
journal= {arXiv preprint arXiv:cond-mat/9411113},
year = {2009}
}
Comments
7 pages, RevTex 3.0, 2 figures available upon request from [email protected], to be published in J.Phys.A Lett