### Abstract

We study Random Walks in an i.i.d. Random Environment (RWRE) defined on b-regular trees. We prove a functional central limit theorem (FCLT) for transient processes, under a moment condition on the environment. We emphasize that we make no uniform ellipticity assumptions. Our approach relies on regenerative levels, i.e. levels that are visited exactly once. On the way, we prove that the distance between consecutive regenerative levels have a geometrically decaying tail. In the second part of this paper, we apply our results to Linearly Edge-Reinforced Random Walk (LERRW) to prove FCLT when the process is defined on b-regular trees, with b≥4, substantially improving the results of the first author (see Theorem 3 of Collevecchio (2006)).

Original language | English |
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Pages (from-to) | 4892-4909 |

Number of pages | 18 |

Journal | Stochastic Processes and their Applications |

Volume | 130 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 2020 |

### Keywords

- Functional central limit theorem
- Random walks in random environment
- Self-interacting random walks

## Cite this

*Stochastic Processes and their Applications*,

*130*(8), 4892-4909. https://doi.org/10.1016/j.spa.2020.02.004