## Abstract

We consider models of random walk in uniformly elliptic i.i.d. random environment in dimension greater than or equal to 4, satisfying a condition slightly weaker than the ballisticity condition (T'). We show that for every ε > 0 and n large enough, the annealed probability of linear slowdown is bounded from above by exp(-(log n)^{d-ε}): This bound almost matches the known lower bound of exp(-C(log n)^{d}; and significantly improves previously known upper bounds. As a corollary we provide almost sharp estimates for the quenched probability of slowdown. As a tool, we show an almost local version of the quenched central limit theorem under the assumption of the same condition.

Original language | English |
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Pages (from-to) | 127-174 |

Number of pages | 48 |

Journal | Journal of the European Mathematical Society |

Volume | 14 |

Issue number | 1 |

DOIs | |

State | Published - 2012 |

Externally published | Yes |