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

2006/01/10 by Martin Zerner, Zerner, Martin P. W.
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #60J10 #60K35 #60K37 #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.math/0601233

openalex publication_date 2006/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate excited random walks on \Z^d, d≥ 1, and on planar strips \Z×\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.

Citations

• Excited random walk in two dimensions has linear speed

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