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Central Limit Theorems for Gromov Hyperbolic Groups

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Abstract

In this paper we study asymptotic properties of symmetric and nondegenerate 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 of F. Ledrappier for certain CAT(−1)-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. Blachère.

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  1. Department of Mathematics, Royal Institute of Technology, Lindstedtsvägen 25, 100 44, Stockholm, Sweden

    Michael Björklund

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  1. Michael Björklund
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Björklund, M. Central Limit Theorems for Gromov Hyperbolic Groups. J Theor Probab 23, 871–887 (2010). https://doi.org/10.1007/s10959-009-0230-x

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  • DOI: https://doi.org/10.1007/s10959-009-0230-x

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