Slowdown estimates and central limit theorem for random walks in random environment |
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Authors: | Alain-Sol Sznitman |
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Institution: | (1) Departement Mathematik, ETH-Zentrum, 8092 Zürich, Switzerland, CH |
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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 ℤ
d
, when d≥2. 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.
Received May 31, 1999 / final version received January 18, 2000?Published online April 19, 2000 |
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Keywords: | Mathematics Subject Classification (1991): 60K40 82D30 |
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