## Abstract

Let (τ)_{x∈ ℤ} ^{d} be i. i. d. random variables with heavy (polynomial) tails. Given a ∈ [0,1], we consider the Markov process defined by the jump rates ω_{x→y} = τ_{x} ^{-(1-a)}τ_{y} ^{a} between two neighbours x and y in ℤ. We give the asymptotic behaviour of the principal eigenvalue of the generator of this process, with Dirichlet boundary condition. The prominent feature is a phase transition that occurs at some threshold depending on the dimension.

Original language | English (US) |
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Pages (from-to) | 227-247 |

Number of pages | 21 |

Journal | Potential Analysis |

Volume | 33 |

Issue number | 3 |

DOIs | |

State | Published - 2010 |

## Keywords

- Distinguished path method
- Phase transition
- Random walk in random environment
- Spectrum
- Trap model

## ASJC Scopus subject areas

- Analysis

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