Rate of growth of a transient cookie random walk

Details Rate of growth of a transient cookie random walk Rate of growth of a transient cookie random walk

2007-03-09

arxiv.org/abs/math/0703275v1

Mathematics

Probability

Scientific paper

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 $\alpha >1$ or $\le 1$. In this article, we give the exact rate of growth of $(X_n)$ in the zero speed regime, namely: for $0<\alpha <1$, $X_n/n^{\frac{\alpha+1}{2}}$ 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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