The infinite valley for a recurrent random walk in random environment

Details The infinite valley for a recurrent random walk in random environment The infinite valley for a recurrent random walk in random environment

2007-08-13

arxiv.org/abs/0708.1739v2

Mathematics

Probability

17 pages, 1 figure

Scientific paper

We consider a one-dimensional recurrent random walk in random environment (RWRE). We show that the - suitably centered - empirical distributions of the RWRE converge weakly to a certain limit law which describes the stationary distribution of a random walk in an infinite valley. The construction of the infinite valley goes back to Golosov. As a consequence, we show weak convergence for both the maximal local time and the self-intersection local time of the RWRE and also determine the exact constant in the almost sure upper limit of the maximal local time.

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