Gromov双曲群的中心极限定理
Central Limit Theorems for Gromov Hyperbolic Groups
摘要：
本文研究了瞬变双曲群上对称和非退化随机游动的渐近性质。证明了随机游动漂移的一个中心极限定理和一个重对数律，推广了S. Sawyer和T. Steger和F.对于某些CAT减去一组的Ledrappier。证明使用了A. Ancona关于双曲群的Martin边界与其Gromov边界的鉴别。我们也给出了一个新的解释，在希尔伯特度量，格林度量，首先介绍了S。Brofferio和S.布莱谢尔
英文摘要：
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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