Infinitely supported Liouville measures of Schreier graphs
Group Theory
2016-08-12 v1 Probability
Abstract
We provide equivalent conditions for Liouville property of actions of groups. As an application, we show that there is a Liouville measure for the action of the Thompson group on dyadic rationals. This result should be compared with a recent result of Kaimanovich, where he shows that the action of the Thompson group F on dyadic rationals is not Liouville for all finitely supported measures. As another application we show that there is a Liouville measure for lamplighter actions. This gives more examples of non-amenable Liouville actions.
Keywords
Cite
@article{arxiv.1608.03554,
title = {Infinitely supported Liouville measures of Schreier graphs},
author = {Kate Juschenko and Tianyi Zheng},
journal= {arXiv preprint arXiv:1608.03554},
year = {2016}
}