Central Limit Theorems for Gromov Hyperbolic Groups

2009/05/08 by Michael Björklund, Bjorklund, Michael · 2 citations
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.0905.1297

openalex publication_date 2009/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study asymptotic properties of symmetric and non-degenerate random walks on transient hyperbolic groups. We prove a central limit theorem and a law of iterated logarithm for the drift of a random walk, extending previous results by S. Sawyer and T. Steger and F. Ledrappier for certain CAT minus one groups. The proofs use a result by A. Ancona on the identification of the Martin boundary of a hyperbolic group with its Gromov boundary. We also give a new interpretation, in terms of Hilbert metrics, of the Green metric, first introduced by S. Brofferio and S. Blachere.

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