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Multi-excited random walks on integers. (English) Zbl 1076.60088
Summary: We introduce a class of nearest-neighbor integer random walks in random and non-random media, which includes excited random walks considered in the literature. At each site the random walker has a drift to the right, the strength of which depends on the environment at that site and on how often the walker has visited that site before. We give exact criteria for recurrence and transience and consider the speed of the walk.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60K37 Processes in random environments
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60G50 Sums of independent random variables; random walks
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