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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107484We 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 $\Z$.12 pages, 1 figureProbability60K35, 60K37, 60J10Recurrence and transience of excited random walks on $\Z^d$ and stripstext