Central Limit Theorems for Gromov Hyperbolic Groups

Details Central Limit Theorems for Gromov Hyperbolic Groups Central Limit Theorems for Gromov Hyperbolic Groups

2009-05-08

arxiv.org/abs/0905.1297v1

Mathematics

Probability

Accepted in Journal of Theoretical Probability

Scientific paper

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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