### Abstract

We consider the simple random walk on Z^{d} evolving in a random i.i.d. potential taking values in [0;+∞). The potential is not assumed integrable, and can be rescaled by a multiplicative factor λ > 0. Completing the work started in a companion paper, we give the asymptotic behaviour of the Lyapunov exponents for d ≥ 3, both annealed and quenched, as the scale parameter λ tends to zero.

Original language | English (US) |
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Article number | 49 |

Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Electronic Journal of Probability |

Volume | 20 |

DOIs | |

State | Published - 2015 |

### Keywords

- Anderson model
- Lyapunov exponents
- Random walk in random potential

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Mountford, T., & Mourrat, J. C. (2015). Lyapunov exponents of random walks in small random potential: The upper bound.

*Electronic Journal of Probability*,*20*, 1-18. [49]. https://doi.org/10.1214/EJP.v20-3489