2016/08/11 by Juschenko, Kate, Zheng, Tianyi
#FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR)
paper · doi:10.48550/arxiv.1608.03554
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 F 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.