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Stuck walks
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  • Published: 02 June 2011

Stuck walks

  • Anna Erschler1,
  • Bálint Tóth2 &
  • Wendelin Werner3,4 

Probability Theory and Related Fields volume 154, pages 149–163 (2012)Cite this article

  • 223 Accesses

  • 6 Citations

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Abstract

We investigate the asymptotic behaviour of a class of self-interacting nearest neighbour random walks on the one-dimensional integer lattice which are pushed by a particular linear combination of their own local time on edges in the neighbourhood of their current position. We prove that in a range of the relevant parameter of the model such random walkers can be eventually confined to a finite interval of length depending on the parameter value. The phenomenon arises as a result of competing self-attracting and self-repelling effects where in the named parameter range the former wins.

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Author information

Authors and Affiliations

  1. Département de Mathématiques, CNRS, Université Paris Sud Orsay, Orsay Cedex, France

    Anna Erschler

  2. Institute of Mathematics, Budapest University of Technology, Budapest, Hungary

    Bálint Tóth

  3. Département de Mathématiques, Université Paris Sud Orsay, Orsay Cedex, France

    Wendelin Werner

  4. DMA, Ecole Normale Supérieure, Paris Cedex 05, France

    Wendelin Werner

Authors
  1. Anna Erschler
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  2. Bálint Tóth
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  3. Wendelin Werner
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Corresponding author

Correspondence to Bálint Tóth.

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Cite this article

Erschler, A., Tóth, B. & Werner, W. Stuck walks. Probab. Theory Relat. Fields 154, 149–163 (2012). https://doi.org/10.1007/s00440-011-0365-4

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  • Received: 15 November 2010

  • Revised: 18 April 2011

  • Published: 02 June 2011

  • Issue Date: October 2012

  • DOI: https://doi.org/10.1007/s00440-011-0365-4

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Keywords

  • Self-interacting random walk
  • Local time
  • Trapping

Mathematics Subject Classification (2010)

  • 60K37
  • 60K99
  • 60J55
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