Volume 9 (2026)
Cantrell, Stephen;  Pollicott, Mark
Central limit theorems for Green metrics on hyperbolic groups
Annales Henri Lebesgue, Volume 9 (2026), pp. 1-32

Metadata

DOI10.5802/ahl.258
Keywords Hyperbolic groups ,  Random walks ,  Central limit theorem

Abstract

Suppose we have two finitely supported, admissible, probability measures on a hyperbolic group $\Gamma $. In this article we prove that the corresponding two Green metrics satisfy a counting central limit theorem when we order the elements of $\Gamma $ according to one of the metrics. Our results also apply to various other metrics including length functions associated to Anosov representations and to group actions on hyperbolic metric spaces.


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