@article{EJP1726,
author = {Jonathon Peterson},
title = {Large deviations and slowdown asymptotics for one-dimensional excited random walks},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {17},
year = {2012},
keywords = {excited random walk; large deviations},
abstract = {We study the large deviations of excited random walks on $\mathbb{Z}$. We prove a large deviation principle for both the hitting times and the position of the random walk and give a qualitative description of the respective rate functions. When the excited random walk is transient with positive speed $v_0$, then the large deviation rate function for the position of the excited random walk is zero on the interval $[0,v_0]$ and so probabilities such as $P(X_n < nv)$ for $v \in (0,v_0)$ decay subexponentially. We show that rate of decay for such slowdown probabilities is polynomial of the order $n^{1-\delta/2}$, where $\delta>2$ is the expected total drift per site of the cookie environment.
},
pages = {no. 48, 1-24},
issn = {1083-6489},
doi = {10.1214/EJP.v17-1726},
url = {http://ejp.ejpecp.org/article/view/1726}}