Convergence of spherical averages for actions of Fuchsian Groups

2018/05/29 by Bufetov, Alexander I., Alexey Klimenko, Klimenko, Alexey +1
Mathematics · #Markov Chains and Monte Carlo Methods #Geometric and Algebraic Topology #Advanced Operator Algebra Research

paper · doi:10.48550/arxiv.1805.11743

Abstract

Pointwise convergence of spherical averages is proved for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen-Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving a reversible Markov chain to which methods previously introduced by the first author for the case of free groups may be applied.

Related

• Convergence of spherical averages for actions of free groups
• Mean convergence of Markovian spherical averages for measure-preserving actions of the free group
• Convergence of noncommutative spherical averages for actions of free groups
• Homogeneous Asymptotic Limits of Uniform Averages on Fuchsian Groups
• Equidistribution in measure-preserving actions of semisimple groups : case of SL₂(ℝ)