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arXiv · 0708.1739

The infinite valley for a recurrent random walk in random environment

Nina Gantert·Yuval Peres·Zhan Shi
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Abstract

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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Nina Gantert, Yuval Peres, Zhan Shi. 2009-02-26. The infinite valley for a recurrent random walk in random environment. https://arxiv.org/abs/0708.1739

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