Principal Eigenvalue for the Random Walk among Random Traps on ?~d

摘要

Let (τ)_(x∈) ?~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 ?. 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.