Electronic Communications in Probability

Recurrence and transience of excited random walks on $Z^d$ and strips

Martin Zerner

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Abstract

We investigate excited random walks on $Z^d, d\ge 1,$ and on planar strips $Z\times{0,1,\ldots,L-1}$ which have a drift in a given direction. The strength of the drift may depend on a random i.i.d. environment and on the local time of the walk. We give exact criteria for recurrence and transience, thus generalizing results by Benjamini and Wilson for once-excited random walk on $Z^d$ and by the author for multi-excited random walk on $Z$.

Article information

Source
Electron. Commun. Probab., Volume 11 (2006), paper no. 12, 118-128.

Dates
Accepted: 7 July 2006
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465058855

Digital Object Identifier
doi:10.1214/ECP.v11-1200

Mathematical Reviews number (MathSciNet)
MR2231739

Zentralblatt MATH identifier
1112.60086

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60K37: Processes in random environments 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Excited Random Walk Recurrence Self-Interacting Random Walk Transience

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

Citation

Zerner, Martin. Recurrence and transience of excited random walks on $Z^d$ and strips. Electron. Commun. Probab. 11 (2006), paper no. 12, 118--128. doi:10.1214/ECP.v11-1200. https://projecteuclid.org/euclid.ecp/1465058855


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