Central Limit Theorems for Gromov Hyperbolic Groups |
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Authors: | Michael Björklund |
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Affiliation: | 1.Department of Mathematics,Royal Institute of Technology,Stockholm,Sweden |
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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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