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Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher
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  • Open Access
  • Published: 05 February 2010

Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher

  • Atilla Yilmaz1 nAff2 

Probability Theory and Related Fields volume 149, pages 463–491 (2011)Cite this article

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Abstract

We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment. It is easy to see that the quenched and the averaged rate functions are not identically equal. When the dimension is at least four and Sznitman’s transience condition (T) is satisfied, we prove that these rate functions are finite and equal on a closed set whose interior contains every nonzero velocity at which the rate functions vanish.

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Acknowledgments

I sincerely thank O. Zeitouni for many valuable discussions and comments.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution,and reproduction in any medium, provided the original author(s) and source are credited.

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Author notes
  1. Atilla Yilmaz

    Present address: Department of Mathematics, University of California, Berkeley, CA, 94720-3840, USA

Authors and Affiliations

  1. Faculty of Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel

    Atilla Yilmaz

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  1. Atilla Yilmaz
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Correspondence to Atilla Yilmaz.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Yilmaz, A. Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher. Probab. Theory Relat. Fields 149, 463–491 (2011). https://doi.org/10.1007/s00440-010-0261-3

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  • Received: 09 March 2009

  • Revised: 31 December 2009

  • Published: 05 February 2010

  • Issue Date: April 2011

  • DOI: https://doi.org/10.1007/s00440-010-0261-3

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Keywords

  • Large deviations
  • Random walk
  • Random environment
  • Disordered media
  • Renewal theorem

Mathematics Subject Classification (2000)

  • 60K37
  • 60F10
  • 82C41
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