Multi-excited random walks on integers

Details Multi-excited random walks on integers Multi-excited random walks on integers

2004-03-03

arxiv.org/abs/math/0403060v1

Mathematics

Probability

25 pages, 3 figures

Scientific paper

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.

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