English

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.

Keywords

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

R2 v1 2026-06-22T18:53:57.515Z