Boundary of the action of Thompson group F on dyadic numbers

2015/12/09 by Pavlo Mishchenko, Mishchenko, Pavlo
Computer Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1512.03083

openalex publication_date 2015/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Poisson boundary of a simple random walk on the Schreier graph of action of F on \mathbbD, where \mathbbD is the set of dyadic numbers in [0, 1], is non-trivial. This gives a new proof of the result of Kaimanovich: Thompson's group F doesn't have Liouville property. In addition, we compute growth function of the Schreier graph of the action of F on \mathbbD.

Related

• Thompson's group F is not Liouville
• Infinitely supported Liouville measures of Schreier graphs
• On spectral properties of the Schreier graphs of the Thompson group F
• Some graphs related to Thompson's group F
• Random walks on dyadic-valued solvable matrix groups