Almost sure estimates for the concentration neighborhood of Sinai's walk

Details Almost sure estimates for the concentration neighborhood of Sinai's walk Almost sure estimates for the concentration neighborhood of Sinai's walk

2005-01-25

arxiv.org/abs/math/0501439v1

Mathematics

Probability

Scientific paper

We consider Sinai's random walk in random environment. We prove that
infinitely often (i.o.) the size of the concentration neighborhood of this
random walk is almost surely bounded. As an application we get that i.o. the
maximal distance between two favorite sites is almost surely bounded.

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