Central limit theorems for Green metrics on hyperbolic groups

2024/04/17 by Cantrell, Stephen, Pollicott, Mark
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2404.11512

Abstract

Suppose we have two finitely supported, admissible, probability measures on a hyperbolic group Γ. In this article we prove that the corresponding two Green metrics satisfy a counting central limit theorem when we order the elements of Γ 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.

Related

• Central limit theorems for counting measures in coarse negative curvature
• Central Limit Theorems for Gromov Hyperbolic Groups
• Central limit theorem and geodesic tracking on hyperbolic spaces and Teichmüller spaces
• Statistical limit laws for hyperbolic groups
• Counting and boundary limit theorems for representations of Gromov-hyperbolic groups