Probability Theory and Related Fields

, Volume 141, Issue 3–4, pp 625–645 | Cite as

On the speed of a cookie random walk



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.


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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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Laboratoire de Probabilités et Modèles AléatoiresUniversité Pierre et Marie Curie, University Paris VIParisFrance

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