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Quenched invariance principle for random walks in balanced random environment
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  • Published: 05 October 2010

Quenched invariance principle for random walks in balanced random environment

  • Xiaoqin Guo1 &
  • Ofer Zeitouni1,2 

Probability Theory and Related Fields volume 152, pages 207–230 (2012)Cite this article

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Abstract

We consider random walks in a balanced random environment in \({\mathbb{Z}^d}\), d ≥ 2. We first prove an invariance principle (for d ≥ 2) and the transience of the random walks when d ≥ 3 (recurrence when d = 2) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for random walks in i.i.d. balanced environments.

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 206 Church St SE, Minneapolis, MN, 55455, USA

    Xiaoqin Guo & Ofer Zeitouni

  2. Faculty of Mathematics, Weizmann Institute, Rehovot, 76100, Israel

    Ofer Zeitouni

Authors
  1. Xiaoqin Guo
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  2. Ofer Zeitouni
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Corresponding author

Correspondence to Xiaoqin Guo.

Additional information

X. Guo’s work was partially supported by NSF grant DMS-0804133.

O. Zeitouni’s work was partially supported by NSF grant DMS-0804133, the Israel Science Foundation and the Herman P. Taubman chair of Mathematics at the Weizmann Institute.

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Guo, X., Zeitouni, O. Quenched invariance principle for random walks in balanced random environment. Probab. Theory Relat. Fields 152, 207–230 (2012). https://doi.org/10.1007/s00440-010-0320-9

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  • Received: 28 April 2010

  • Revised: 29 August 2010

  • Published: 05 October 2010

  • Issue Date: February 2012

  • DOI: https://doi.org/10.1007/s00440-010-0320-9

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Keywords

  • Random walks in random environments
  • Homogenization
  • Maximum principle
  • Mean value inequality
  • Percolation

Mathematics Subject Classification (2000)

  • 60K37
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