Word metric asymptotics for actions of hyperbolic groups on Gromov hyperbolic spaces
Ilya Gekhtman (Rheinische Friedrich-Wilhelms-Universität Bonn)
MSRI: Simons Auditorium
I will discuss work in progress with Sam Taylor and Giulio Tiozzo in which we study some asymptotics with respect to the word metric for actions of hyperbolic groups on Gromov hyperbolic spaces. For example for a large class of such actions we prove that the proportion of elements in a Cayley ball of radius R which do not act loxodromically decays to zero.