Electronic Journal of Probability

Excited Random Walk on Trees

Stanislav Volkov

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Abstract

We consider a nearest-neighbor stochastic process on a rooted tree $G$ which goes toward the root with probability $1-\varepsilon$ when it visits a vertex for the first time. At all other times it behaves like a simple random walk on $G$. We show that for all $\varepsilon\ge 0$ this process is transient. Also we consider a generalization of this process and establish its transience in some cases.

Article information

Source
Electron. J. Probab., Volume 8 (2003), paper no. 23, 15 p.

Dates
First available in Project Euclid: 23 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464037596

Digital Object Identifier
doi:10.1214/EJP.v8-180

Mathematical Reviews number (MathSciNet)
MR2041824

Zentralblatt MATH identifier
1065.60097

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Citation

Volkov, Stanislav. Excited Random Walk on Trees. Electron. J. Probab. 8 (2003), paper no. 23, 15 p. doi:10.1214/EJP.v8-180. https://projecteuclid.org/euclid.ejp/1464037596


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References

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The Institute of Mathematical Statistics and the Bernoulli Society

Electronic Journal of Probability

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