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2012 Large deviations and slowdown asymptotics for one-dimensional excited random walks
Jonathon Peterson
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Electron. J. Probab. 17: 1-24 (2012). DOI: 10.1214/EJP.v17-1726


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. 


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Jonathon Peterson. "Large deviations and slowdown asymptotics for one-dimensional excited random walks." Electron. J. Probab. 17 1 - 24, 2012.


Accepted: 21 June 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1260.60184
MathSciNet: MR2946155
Digital Object Identifier: 10.1214/EJP.v17-1726

Primary: 60K35
Secondary: 60F10 , 60K37

Keywords: excited random walk , large deviations


Vol.17 • 2012
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