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On the speed of a cookie random walk
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  • Published: 08 August 2007

On the speed of a cookie random walk

  • Anne-Laure Basdevant1 &
  • Arvind Singh1 

Probability Theory and Related Fields volume 141, pages 625–645 (2008)Cite this article

Abstract

We consider the model of the one-dimensional cookie random walk when the initial cookie distribution is spatially uniform and the number of cookies per site is finite. We give a criterion to decide whether the limiting speed of the walk is non-zero. In particular, we show that a positive speed may be obtained for just three cookies per site. We also prove a result on the continuity of the speed with respect to the initial cookie distribution.

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Author information

Authors and Affiliations

  1. Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, University Paris VI, 175 rue du Chevaleret, 75013, Paris, France

    Anne-Laure Basdevant & Arvind Singh

Authors
  1. Anne-Laure Basdevant
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  2. Arvind Singh
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Corresponding author

Correspondence to Arvind Singh.

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Cite this article

Basdevant, AL., Singh, A. On the speed of a cookie random walk. Probab. Theory Relat. Fields 141, 625–645 (2008). https://doi.org/10.1007/s00440-007-0096-8

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  • Received: 22 November 2006

  • Revised: 03 July 2007

  • Published: 08 August 2007

  • Issue Date: July 2008

  • DOI: https://doi.org/10.1007/s00440-007-0096-8

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Keywords

  • Law of large numbers
  • Cookie or multi-excited random walk
  • Branching process with migration

Mathematics Subject Classification (2000)

  • 60K35
  • 60J80
  • 60F15
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