Rate of growth of a transient cookie random walk

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 $\alpha >1$ 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.

Cited by in corpus (2)

• A note on multi-type cookie random walk on integers
• Positively and negatively excited random walks on integers, with branching processes