Central Limit Theorems for Gromov Hyperbolic Groups

Michael Bjorklund

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arXiv · 0905.1297

Central Limit Theorems for Gromov Hyperbolic Groups

Michael Bjorklund

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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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Michael Bjorklund. 2009-05-08. Central Limit Theorems for Gromov Hyperbolic Groups. https://arxiv.org/abs/0905.1297

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