Open Access
2006 Recurrence and transience of excited random walks on $Z^d$ and strips
Martin Zerner
Author Affiliations +
Electron. Commun. Probab. 11: 118-128 (2006). DOI: 10.1214/ECP.v11-1200


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 $Z$.


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Martin Zerner. "Recurrence and transience of excited random walks on $Z^d$ and strips." Electron. Commun. Probab. 11 118 - 128, 2006.


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

zbMATH: 1112.60086
MathSciNet: MR2231739
Digital Object Identifier: 10.1214/ECP.v11-1200

Primary: 60K35
Secondary: 60J10 , 60K37

Keywords: excited random walk , recurrence , Self-interacting random walk , transience

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