Random walks on the discrete affine group
Group Theory
2017-10-27 v2 Probability
Abstract
We introduce the discrete affine group of a regular tree as a finitely generated subgroup of the affine group. We describe the Poisson boundary of random walks on it as a space of configurations. We compute isoperimetric profile and Hilbert compression exponent of the group. We also discuss metric relationship with some lamplighter groups and lamplighter graphs.
Cite
@article{arxiv.1703.07741,
title = {Random walks on the discrete affine group},
author = {Jérémie Brieussel and Ryokichi Tanaka and Tianyi Zheng},
journal= {arXiv preprint arXiv:1703.07741},
year = {2017}
}
Comments
The introduction has been rewritten