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 ωx→y = τx -(1-a)τy 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.
- Distinguished path method
- Phase transition
- Random walk in random environment
- Trap model
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