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

Slowdown estimates and central limit theorem for random walks in random environment 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

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

, Volume 2 (2) – Jun 1, 2000
51 pages

/lp/springer-journals/slowdown-estimates-and-central-limit-theorem-for-random-walks-in-pMRl4dvm0Z
Publisher
Springer Journals
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/s100970050001
Publisher site
See Article on Publisher Site

### 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.

### Journal

Journal of the European Mathematical SocietySpringer Journals

Published: Jun 1, 2000