Electronic Communications in Probability

A relation between dimension of the harmonic measure, entropy and drift for a random walk on a hyperbolic space

Vincent Le Prince

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Abstract

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, where only an upper bound for the dimension was proved.

Article information

Source
Electron. Commun. Probab., Volume 13 (2008), paper no. 5, 45-53.

Dates
Accepted: 2 February 2008
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465233432

Digital Object Identifier
doi:10.1214/ECP.v13-1350

Mathematical Reviews number (MathSciNet)
MR2386061

Zentralblatt MATH identifier
1189.60094

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 20F67: Hyperbolic groups and nonpositively curved groups 28D20: Entropy and other invariants 28A78: Hausdorff and packing measures

Keywords
Random walk hyperbolic space harmonic measure entropy drift

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Le Prince, Vincent. A relation between dimension of the harmonic measure, entropy and drift for a random walk on a hyperbolic space. Electron. Commun. Probab. 13 (2008), paper no. 5, 45--53. doi:10.1214/ECP.v13-1350. https://projecteuclid.org/euclid.ecp/1465233432


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