The Poisson boundary of a locally discrete group of diffeomorphisms of the circle

TL;DR

This paper determines the Poisson boundary for certain groups of circle diffeomorphisms, providing insights into their probabilistic and geometric properties.

Contribution

It explicitly computes the Poisson boundary for locally discrete groups of circle diffeomorphisms, a novel result in the study of group boundaries.

Findings

Identification of the Poisson boundary for these groups

New methods for analyzing group actions on the circle

Enhanced understanding of harmonic functions on these groups

Abstract

We compute the Poisson boundary of locally discrete groups of diffeomorphisms of the circle.