Journal of the European Mathematical Society


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Volume 2, Issue 2, 2000, pp. 93–143
DOI: 10.1007/s100970050001

Slowdown estimates and central limit theorem for random walks in random environment

Alain-Sol Sznitman[1]

(1) Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092, ZÜRICH, SWITZERLAND

Abstract. This work is concerned with asymptotic properties of multi-dimensional random walks in random environment. Under Kalikow's condition, we show a central limit theorem for random walks in random environment on Êd, when dS2. We also derive tail estimates on the probability of slowdowns. These latter estimates are of special interest due to the natural interplay between slowdowns and the presence of traps in the medium. The tail behavior of the renewal time constructed in [25] plays an important role in the investigation of both problems. This article also improves the previous work of the author [24], concerning estimates of probabilities of slowdowns for walks which are neutral or biased to the right.

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Sznitman Alain-Sol: Slowdown estimates and central limit theorem for random walks in random environment. J. Eur. Math. Soc. 2 (2000), 93-143. doi: 10.1007/s100970050001