Random walk on Bethe lattice and hyperbolic geometry
Condensed Matter
2009-10-28 v2
Abstract
We give the exact solution to the problem of a random walk on the Bethe lattice through a mapping on an asymmetric random walk on the half-line. We also study the continuous limit of this model, and discuss in detail the relation between the random walk on the Bethe lattice and Brownian motion on a space of constant negative curvature.
Keywords
Cite
@article{arxiv.cond-mat/9509067,
title = {Random walk on Bethe lattice and hyperbolic geometry},
author = {Cecile Monthus and Chistophe Texier},
journal= {arXiv preprint arXiv:cond-mat/9509067},
year = {2009}
}
Comments
12 pages. Revised version (minor changes) to appear in J. Phys. A