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

Ilya Gekhtman

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arXiv · 1711.04985

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

Ilya Gekhtman

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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.

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Ilya Gekhtman. 2017-11-14. Equidistribution of closed geodesics along random walk trajectories with respect to the harmonic invariant measure. https://arxiv.org/abs/1711.04985

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