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

Abstract

We investigate excited random walks on ${\mathbb{Z}}^d,d\ge 1,$ and on planar strips $\mathbb{Z}\times \{0,1,...,L-1\}$ 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 ${\mathbb{Z}}^d$ and by the author for multi-excited random walk on $\mathbb{Z}$.

12 pages, 1 figure

References in corpus (3)

• Excited Random Walk in One Dimension
• Excited random walk in two dimensions has linear speed
• Excited random walk against a wall