Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 13 (2008), paper no. 5, 45-53.
A relation between dimension of the harmonic measure, entropy and drift for a random walk on a hyperbolic space
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.
Electron. Commun. Probab., Volume 13 (2008), paper no. 5, 45-53.
Accepted: 2 February 2008
First available in Project Euclid: 6 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
This work is licensed under aCreative Commons Attribution 3.0 License.
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