Random walks on free solvable groups
Probability
2013-07-23 v1
Abstract
For any finitely generated group G, let n ---> \Phi_G(n) be the function that describes the rough asymptotic behavior of the probability of return to the identity element at time 2n of a symmetric simple random walk on G (this is an invariant of quasi-isometry). We determine this function when G is the free solvable group S_{d,r} of derived length d on r generators and some other related groups.
Cite
@article{arxiv.1307.5332,
title = {Random walks on free solvable groups},
author = {Laurent Saloff-Coste and Tianyi Zheng},
journal= {arXiv preprint arXiv:1307.5332},
year = {2013}
}