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Large deviations and slowdown asymptotics for one-dimensional excited random walks


 
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1. Title Title of document Large deviations and slowdown asymptotics for one-dimensional excited random walks
 
2. Creator Author's name, affiliation, country Jonathon Peterson; Purdue University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) excited random walk; large deviations
 
3. Subject Subject classification 60K35; 60F10; 60K37
 
4. Description 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. 
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF
 
7. Date (YYYY-MM-DD) 2012-06-21
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1726
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1726
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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