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Strong localization and macroscopic atoms for directed polymers
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  • Published: 22 November 2006

Strong localization and macroscopic atoms for directed polymers

  • Vincent Vargas1 

Probability Theory and Related Fields volume 138, pages 391–410 (2007)Cite this article

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Abstract

In this article, we derive strong localization results for directed polymers in random environment. We show that at “low temperature” the polymer measure is asymptotically concentrated at a few points of macroscopic mass (we call these points \({\epsilon}\) -atoms). These results are derived assuming weak conditions on the tail decay of the random environment.

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Author information

Authors and Affiliations

  1. Mathématiques, case 7012, Université Paris 7, 2, place Jussieu, 75251, Paris, France

    Vincent Vargas

Authors
  1. Vincent Vargas
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Corresponding author

Correspondence to Vincent Vargas.

Additional information

Partially supported by CNRS (UMR 7599 “Probabilités et Modèles Aléatoires”).

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Cite this article

Vargas, V. Strong localization and macroscopic atoms for directed polymers. Probab. Theory Relat. Fields 138, 391–410 (2007). https://doi.org/10.1007/s00440-006-0030-5

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  • Received: 13 March 2006

  • Revised: 06 September 2006

  • Published: 22 November 2006

  • Issue Date: July 2007

  • DOI: https://doi.org/10.1007/s00440-006-0030-5

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Keywords

  • Directed polymers in random environment

Mathematics Subject Classification (2000)

  • 60K37
  • 82B44
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