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Quenched invariance principles for walks on clusters of percolation or among random conductances
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  • Published: 25 March 2004

Quenched invariance principles for walks on clusters of percolation or among random conductances

  • Vladas Sidoravicius1 &
  • Alain-Sol Sznitman2 

Probability Theory and Related Fields volume 129, pages 219–244 (2004)Cite this article

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Abstract.

In this work we principally study random walk on the supercritical infinite cluster for bond percolation on ℤd. We prove a quenched functional central limit theorem for the walk when d≥4. We also prove a similar result for random walk among i.i.d. random conductances along nearest neighbor edges of ℤd, when d≥1.

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Authors and Affiliations

  1. IMPA, Estrada Dona Castorina 110, Jardim Botanico, CEP 22460-320, Rio de Janeiro, RJ, Brasil

    Vladas Sidoravicius

  2. Departement Mathematik, ETH-Zentrum, CH-8092, Zürich, Switzerland

    Alain-Sol Sznitman

Authors
  1. Vladas Sidoravicius
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  2. Alain-Sol Sznitman
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Corresponding author

Correspondence to Vladas Sidoravicius.

Additional information

V. Sidoravicius would like to thank the FIM for financial support and hospitality during his multiple visits to ETH. His research was also partially supported by FAPERJ and CNPq.

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Sidoravicius, V., Sznitman, AS. Quenched invariance principles for walks on clusters of percolation or among random conductances. Probab. Theory Relat. Fields 129, 219–244 (2004). https://doi.org/10.1007/s00440-004-0336-0

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  • Received: 08 June 2003

  • Revised: 17 December 2003

  • Published: 25 March 2004

  • Issue Date: June 2004

  • DOI: https://doi.org/10.1007/s00440-004-0336-0

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Keywords

  • Random Walk
  • Limit Theorem
  • Central Limit
  • Central Limit Theorem
  • Invariance Principle
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