Rate of growth of a transient cookie random walk

@inproceedings{Basdevant2008RateOG,
  title={Rate of growth of a transient cookie random walk},
  author={Anne-Laure Basdevant and Arvind Singh},
  year={2008}
}
We consider a one-dimensional transient cookie random walk. It is known from a previous paper [3] 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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