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

Martin P. W. Zerner

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arXiv · math/0601233

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

Martin P. W. Zerner

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Abstract

We investigate excited random walks on $\Z^d, d\ge 1,$ and on planar strips $\Z\times\{0,1,...,L-1\}$ 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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BibTeX RIS

Martin P. W. Zerner. 2006-01-10. Recurrence and transience of excited random walks on $\Z^d$ and strips. https://arxiv.org/abs/math/0601233

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