Electronic Journal of Probability

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

Jonathon Peterson

Full-text: Open access

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. 

Article information

Source
Electron. J. Probab., Volume 17 (2012), paper no. 48, 24 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465062370

Digital Object Identifier
doi:10.1214/EJP.v17-1726

Mathematical Reviews number (MathSciNet)
MR2946155

Zentralblatt MATH identifier
1260.60184

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60F10: Large deviations 60K37: Processes in random environments

Keywords
excited random walk large deviations

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Peterson, Jonathon. Large deviations and slowdown asymptotics for one-dimensional excited random walks. Electron. J. Probab. 17 (2012), paper no. 48, 24 pp. doi:10.1214/EJP.v17-1726. https://projecteuclid.org/euclid.ejp/1465062370


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