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Invariance principle for the random conductance model
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  • Published: 12 June 2012

Invariance principle for the random conductance model

  • S. Andres1,
  • M. T. Barlow2,
  • J.-D. Deuschel3 &
  • …
  • B. M. Hambly4 

Probability Theory and Related Fields volume 156, pages 535–580 (2013)Cite this article

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Abstract

We study a continuous time random walk X in an environment of i.i.d. random conductances \({\mu_{e} \in [0,\infty)}\) in \({\mathbb{Z}^d}\) . We assume that \({\mathbb{P}(\mu_{e} > 0) > p_c}\) , so that the bonds with strictly positive conductances percolate, but make no other assumptions on the law of the μ e . We prove a quenched invariance principle for X, and obtain Green’s functions bounds and an elliptic Harnack inequality.

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    S. Andres

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

    M. T. Barlow

  3. Fachbereich Mathematik, Technische Universitat Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    J.-D. Deuschel

  4. Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford, OX1 3LB, UK

    B. M. Hambly

Authors
  1. S. Andres
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  2. M. T. Barlow
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  3. J.-D. Deuschel
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  4. B. M. Hambly
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Corresponding author

Correspondence to J.-D. Deuschel.

Additional information

S. Andres and M. T. Barlow were partially supported by NSERC (Canada), J.-D. Deuschel was partially supported by DFG (Germany).

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Andres, S., Barlow, M.T., Deuschel, JD. et al. Invariance principle for the random conductance model. Probab. Theory Relat. Fields 156, 535–580 (2013). https://doi.org/10.1007/s00440-012-0435-2

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  • Received: 19 May 2011

  • Revised: 13 May 2012

  • Published: 12 June 2012

  • Issue Date: August 2013

  • DOI: https://doi.org/10.1007/s00440-012-0435-2

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Keywords

  • Random conductance model
  • Heat kernel
  • Invariance principle
  • Ergodic
  • Corrector

Mathematics Subject Classification (2000)

  • 60K37
  • 60F17
  • 82C41
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