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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 26 open journal systems 


Rate of growth of a transient cookie random walk

Anne-Laure Basdevant, Université Paris VI
Arvind Singh, Université Paris VI


Abstract
We consider a one-dimensional transient cookie random walk. It is known from a previous paper (BS2008) that a cookie random walk (Xn) has positive or zero speed according to some positive parameter α >1 or ≤ 1. In this article, we give the exact rate of growth of Xn in the zero speed regime, namely: for 0<α<1, Xn/n(α+1)/2 converges in law to a Mittag-Leffler distribution whereas for α=1, Xn(log n)/n converges in probability to some positive constant.


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Pages: 811-851

Published on: May 7, 2008
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Electronic Journal of Probability. ISSN: 1083-6489