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Convergence to fractional kinetics for random walks associated with unbounded conductances

Barlow, Martin ; Černý, Jiří

In: Probability Theory and Related Fields, 2011, vol. 149, no. 3-4, p. 639-673

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    Titre
    • Convergence to fractional kinetics for random walks associated with unbounded conductances
    Auteur
    • Barlow, Martin. Department of Mathematics, University of British Columbia, V6T 1Z2, Vancouver, BC, Canada
    • Černý, Jiří. Department of Mathematics, ETH Zürich, Rämistr. 101, 8092, Zurich, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Probability Theory and Related Fields, 2011, vol. 149, no. 3-4, p. 639-673. Springer-Verlag
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:317520
    Summary
    We consider a random walk among unbounded random conductances whose distribution has infinite expectation and polynomial tail. We prove that the scaling limit of this process is a Fractional-Kinetics process—that is the time change of a d-dimensional Brownian motion by the inverse of an independent α-stable subordinator. We further show that the same process appears in the scaling limit of the non-symmetric Bouchaud's trap model