Statistical Hyperbolicity of Relatively Hyperbolic Groups

Abstract

In this work, we begin by defining what it means for a group to be statistically hyperbolic. We then give several examples of groups, including non-elementary hyperbolic groups, which either are statistically hyperbolic or are not. Following that, we define what it means for a group to be relatively hyperbolic. Finally, in the main portion of this work, we show that groups which are relatively hyperbolic, with a few additional conditions in place, must also be statistically hyperbolic.