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Random walks on hyperbolic spaces
We will be interested in the radial behavior of random walks on non-elementary isometry groups of Gromov hyperbolic spaces. It is a well-known fact that non-degenerate symmetric walks tend to infinity with a linear rate. More qualitative statements ( CLT, LIL etc. ) for random walks on trees has been proved by several authors. We extend these results to hyperbolic spaces under some weak conditions.
The conditions are inspired by the works of A. Ancona on the Martin boundary of hyperbolic graphs and manifolds.
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