Growth Series and Random Walks on Some Hyperbolic Graphs
Group Theory
2009-11-27 v2
Abstract
Consider the tesselation of the hyperbolic plane by m-gons, l per vertex. In its 1-skeleton, we compute the growth series of vertices, geodesics, tuples of geodesics with common extremities. We also introduce and enumerate "holly trees", a family of reduced loops in these graphs. We then apply Grigorchuk's result relating cogrowth and random walks to obtain lower estimates on the spectral radius of the Markov operator associated with a symmetric random walk on these graphs.
Cite
@article{arxiv.math/0109069,
title = {Growth Series and Random Walks on Some Hyperbolic Graphs},
author = {Laurent Bartholdi and Tullio G. Ceccherini-Silberstein},
journal= {arXiv preprint arXiv:math/0109069},
year = {2009}
}
Comments
21 pages. to appear in monash. math