## Abstract

Let (G,μ) be a discrete group equipped with a generating probability measure, and let Γ be a finite index subgroup of G. A μ -random walk on G, starting from the identity, returns to Γ with probability one. Let θ be the hitting measure, or the distribution of the position in which the random walk first hits Γ. We prove that the Furstenberg entropy of a (G,μ)-stationary space, with respect to the action of (Γ, θ), is equal to the Furstenberg entropy with respect to the action of (G,μ), times the index of Γ in G. The index is shown to be equal to the expected return time to Γ. As a corollary, when applied to the Furstenberg-Poisson boundary of (G,μ), we prove that the random walk entropy of (Γ, θ) is equal to the random walk entropy of (G,μ), times the index of Γ in G.

Original language | English |
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Pages (from-to) | 837-853 |

Number of pages | 17 |

Journal | Ergodic Theory and Dynamical Systems |

Volume | 34 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jan 2014 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics