Principal Eigenvalue for the Random Walk among Random Traps on ℤd

Jean Christophe Mourrat

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish (US)
Pages (from-to)227-247
Number of pages21
JournalPotential Analysis
Volume33
Issue number3
DOIs
StatePublished - 2010

Keywords

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

ASJC Scopus subject areas

  • Analysis

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