Random walks on hyperbolic groups and their Riemann surfaces
数学物理
2007-05-23 v1 统计力学
math.MP
摘要
We investigate invariants for random elements of different hyperbolic groups. We provide a method, using Cayley graphs of groups, to compute the probability distribution of the minimal length of a random word, and explicitly compute the drift in different cases, including the braid group . We also compute in this case the return probability. The action of these groups on the hyperbolic plane is investigated, and the distribution of a geometric invariant, the hyperbolic distance, is given. These two invariants are shown to be related by a closed formula.
引用
@article{arxiv.math-ph/0012037,
title = {Random walks on hyperbolic groups and their Riemann surfaces},
author = {Sergei Nechaev and Raphael Voituriez},
journal= {arXiv preprint arXiv:math-ph/0012037},
year = {2007}
}
备注
29 pages, 8 figures