Statistical hyperbolicity of relatively hyperbolic groups

TL;DR

This paper proves that non-elementary relatively hyperbolic groups are statistically hyperbolic across all finite generating sets and extends this property to certain direct products involving such groups.

Contribution

It establishes the statistical hyperbolicity of relatively hyperbolic groups and some of their direct products, broadening understanding of their geometric properties.

Findings

Non-elementary relatively hyperbolic groups are statistically hyperbolic with respect to any finite generating set.

Statistical hyperbolicity is also shown for certain direct products involving relatively hyperbolic groups.

Abstract

We prove that a non-elementary relatively hyperbolic group is statistically hyperbolic with respect to every finite generating set. We also establish statistical hyperbolicity for certain direct products of two groups, one of which is relatively hyperbolic.