We study the large deviations of one-dimensional excited random walks. 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 v0β,
then the large deviation rate function for the position of the excited random
walk is zero on the interval [0,v0β] and so probabilities such as P(Xnβ<nv) for vβ(0,v0β) decay subexponentially. We show that rate of decay for
such slowdown probabilities is polynomial of the order n1βΞ΄/2, where
Ξ΄>2 is the expected total drift per site of the cookie environment.Comment: 23 pages, 3 figure