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On the speed of a cookie random walk

By Anne-Laure Basdevant and Arvind Singh

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 3 cookies per site. We also prove a result on the continuity of the speed with respect to the initial cookie distribution

Topics: law of large numbers, cookie or multi-excited random walk, branching process with migration, AMS 60K35, 60J80, 60F15, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR]
Publisher: HAL CCSD
Year: 2006
OAI identifier: oai:HAL:hal-00114953v1
Provided by: Hal-Diderot
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