The ergodic theory of hyperbolic groups

TL;DR

This paper provides a comprehensive introduction to the use of dynamical and probabilistic methods in studying hyperbolic groups, including some new proofs and broader generalizations of existing results.

Contribution

It offers a self-contained presentation with novel proofs and extends some results in the theory of hyperbolic groups using dynamical and probabilistic techniques.

Findings

New proofs of existing results

Broader generality of some theorems

Enhanced understanding of hyperbolic groups through dynamical methods

Abstract

These notes are a self-contained introduction to the use of dynamical and probabilistic methods in the study of hyperbolic groups. Most of this material is standard; however some of the proofs given are new, and some results are proved in greater generality than have appeared in the literature. These notes originated in a minicourse given at a workshop in Melbourne, July 11-15 2011.