### Abstract

ℒ denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on ℒ is harmonic if and only if it is the projection of a measure on the unit tangent bundle T^{1} ℒ of ℒ which is invariant under both the geodesic and the horocycle flows.

Original language | English (US) |
---|---|

Pages (from-to) | 1078-1089 |

Number of pages | 12 |

Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |

Volume | 44 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2008 |

### Fingerprint

### Keywords

- Brownian Motion on the hyperbolic plane
- Foliated spaces
- Geodesic flow
- Harmonic measures
- Horocycle flow

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces.** / Bakhtin, Yuri; Martínez, Matilde.

Research output: Contribution to journal › Article

*Annales de l'institut Henri Poincare (B) Probability and Statistics*, vol. 44, no. 6, pp. 1078-1089. https://doi.org/10.1214/07-AIHP147

}

TY - JOUR

T1 - A characterization of harmonic measures on laminations by hyperbolic Riemann surfaces

AU - Bakhtin, Yuri

AU - Martínez, Matilde

PY - 2008/12/1

Y1 - 2008/12/1

N2 - ℒ denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on ℒ is harmonic if and only if it is the projection of a measure on the unit tangent bundle T1 ℒ of ℒ which is invariant under both the geodesic and the horocycle flows.

AB - ℒ denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on ℒ is harmonic if and only if it is the projection of a measure on the unit tangent bundle T1 ℒ of ℒ which is invariant under both the geodesic and the horocycle flows.

KW - Brownian Motion on the hyperbolic plane

KW - Foliated spaces

KW - Geodesic flow

KW - Harmonic measures

KW - Horocycle flow

UR - http://www.scopus.com/inward/record.url?scp=77951825493&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951825493&partnerID=8YFLogxK

U2 - 10.1214/07-AIHP147

DO - 10.1214/07-AIHP147

M3 - Article

VL - 44

SP - 1078

EP - 1089

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

SN - 0246-0203

IS - 6

ER -