On the speed of a cookie random walk
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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.
KeywordsLaw of large numbers Cookie or multi-excited random walk Branching process with migration
Mathematics Subject Classification (2000)60K35 60J80 60F15
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