### Abstract

Attributing a positive value ?x to each x ∈ ℤ^{d} , we investigate a nearest-neighbour random walk which is reversible for the measure with weights (τ_{x} ), often known as "Bouchaud's trap model."We assume that these weights are independent, identically distributed and non-integrable random variables (with polynomial tail), and that d ≥ 5.We obtain the quenched subdiffusive scaling limit of the model, the limit being the fractional kinetics process. We begin our proof by expressing the random walk as the time change of a random walk among random conductances. We then focus on proving that the time change converges, under the annealed measure, to a stable subordinator. This is achieved using previous results concerning the mixing properties of the environment viewed by the time-changed random walk.

Original language | English (US) |
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Pages (from-to) | 813-849 |

Number of pages | 37 |

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

Volume | 47 |

Issue number | 3 |

DOIs | |

State | Published - Aug 2011 |

### Keywords

- Fractional kinetics
- Random walk in random environment
- Stable process
- Trap model

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

^{d}.

*Annales de l'institut Henri Poincare (B) Probability and Statistics*,

*47*(3), 813-849. https://doi.org/10.1214/10-AIHP387