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Convergence to fractional kinetics for random walks associated with unbounded conductances
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  • Published: 02 December 2009

Convergence to fractional kinetics for random walks associated with unbounded conductances

  • Martin T. Barlow1 &
  • Jiří Černý2 

Probability Theory and Related Fields volume 149, pages 639–673 (2011)Cite this article

An Erratum to this article was published on 11 February 2011

Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Martin T. Barlow

  2. Department of Mathematics, ETH Zürich, Rämistr. 101, 8092, Zurich, Switzerland

    Jiří Černý

Authors
  1. Martin T. Barlow
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  2. Jiří Černý
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Corresponding author

Correspondence to Jiří Černý.

Additional information

Research partially supported by NSERC (Canada).

An erratum to this article can be found at http://dx.doi.org/10.1007/s00440-011-0344-9

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Barlow, M.T., Černý, J. Convergence to fractional kinetics for random walks associated with unbounded conductances. Probab. Theory Relat. Fields 149, 639–673 (2011). https://doi.org/10.1007/s00440-009-0257-z

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  • Received: 15 January 2009

  • Revised: 17 November 2009

  • Published: 02 December 2009

  • Issue Date: April 2011

  • DOI: https://doi.org/10.1007/s00440-009-0257-z

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Mathematics Subject Classification (2000)

  • 60F17
  • 60K37
  • 82C41
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