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Rate of growth of a transient cookie random walk

Anne-Laure Basdevant·Arvind Singh
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Abstract

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

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Anne-Laure Basdevant, Arvind Singh. 2007-03-09. Rate of growth of a transient cookie random walk. https://arxiv.org/abs/math/0703275

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