Equidistribution of closed geodesics along random walk trajectories with respect to the harmonic invariant measure

Abstract

We prove that for suitable random walks on isometry groups of $CAT(-1)$ spaces, typical sample paths eventually land on loxodromic elements which equidistribute with respect to a flow invariant measure on the unit tangent bundle of the quotient space.

References in corpus (1)

• Martin boundary covers Floyd boundary