## Recurrence and transience of excited random walks on $$\mathbb Z^d$$ and strips.(English)Zbl 1112.60086

Summary: We investigate excited random walks on $$\mathbb Z^d$$, $$d\geq 1,$$ and on planar strips $$\mathbb Z\times\{0,1,\dots,L-1\}$$ 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 I. Benjamini and D. B. Wilson [Electron. Commun. Probab. 8, 86–92 (2003; Zbl 1060.60043)] for once-excited random walk on $$\mathbb Z^d$$ and by the author [Probab. Theory Relat. Fields 133, No. 1, 98–122 (2005; Zbl 1076.60088)] for multi-excited random walk on $$\mathbb Z$$.

### MSC:

 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60G50 Sums of independent random variables; random walks 60K37 Processes in random environments

### Citations:

Zbl 1060.60043; Zbl 1076.60088
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