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 $(X_n)$ has positive or zero speed according to some positive parameter $\alpha >1$ or $\leq 1$. In this article, we give the exact rate of growth of $X_n$ in the zero speed regime, namely: for $0<\alpha<1$, $X_n/n^{(α+1)/2}$ converges in law to a Mittag-Leffler distribution whereas for $\alpha=1$, $X_n(\log n)/n$ converges in probability to some positive constant.

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Pages: 811-851

Publication Date: May 7, 2008

DOI: 10.1214/EJP.v13-498

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