Scaling limit of the random walk among random traps on ℤd

Jean Christophe Mourrat

Research output: Contribution to journalArticle

Abstract

Attributing a positive value ?x to each x ∈ ℤd , we investigate a nearest-neighbour random walk which is reversible for the measure with weights (τx ), often known as "Bouchaud's trap model."We assume that these weights are independent, identically distributed and non-integrable random variables (with polynomial tail), and that d ≥ 5.We obtain the quenched subdiffusive scaling limit of the model, the limit being the fractional kinetics process. We begin our proof by expressing the random walk as the time change of a random walk among random conductances. We then focus on proving that the time change converges, under the annealed measure, to a stable subordinator. This is achieved using previous results concerning the mixing properties of the environment viewed by the time-changed random walk.

Original languageEnglish (US)
Pages (from-to)813-849
Number of pages37
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume47
Issue number3
DOIs
StatePublished - Aug 2011

Keywords

  • Fractional kinetics
  • Random walk in random environment
  • Stable process
  • Trap model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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