@article{EJP498,
author = {Anne-Laure Basdevant and Arvind Singh},
title = {Rate of growth of a transient cookie random walk},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {13},
year = {2008},
keywords = {Rates of transience; cookie or multi-excited random walk; branching process with migration},
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.},
pages = {no. 26, 811-851},
issn = {1083-6489},
doi = {10.1214/EJP.v13-498},
url = {http://ejp.ejpecp.org/article/view/498}}