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A relation between dimension of the harmonic measure, entropy and drift for a random walk on a hyperbolic space. (English) Zbl 1189.60094
Summary: We establish in this paper an exact formula which links the dimension of the harmonic measure, the asymptotic entropy and the rate of escape for a random walk on a discrete subgroup of the isometry group of a Gromov hyperbolic space. This completes a result obtained by the author in a previous paper [Trans. Am. Math. Soc. 359, No. 6, 2881–2898 (2007; Zbl 1126.60036)], where only an upper bound for the dimension was proved.

MSC:
60G50 Sums of independent random variables; random walks
20F67 Hyperbolic groups and nonpositively curved groups
28D20 Entropy and other invariants
28A78 Hausdorff and packing measures
Citations:
Zbl 1126.60036
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