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

Alain-Sol Sznitman

Journal of the European Mathematical Society (2000)

  • Volume: 002, Issue: 2, page 93-143
  • ISSN: 1435-9855

Abstract

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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 previouswork of the author [24], concerning estimates of probabilities of slowdowns for walks which are neutral or biased to the right.

How to cite

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Sznitman, Alain-Sol. "Slowdown estimates and central limit theorem for random walks in random environment." Journal of the European Mathematical Society 002.2 (2000): 93-143. <http://eudml.org/doc/277558>.

@article{Sznitman2000,
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 $\mathbb \{Z\}^d$, 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 previouswork of the author [24], concerning estimates of probabilities of slowdowns for walks which are neutral or biased to the right.},
author = {Sznitman, Alain-Sol},
journal = {Journal of the European Mathematical Society},
keywords = {multi-dimensional random walk; Kalikow’s condition; slowdown; trap; random walks in random environment; central limit theorem; large deviations},
language = {eng},
number = {2},
pages = {93-143},
publisher = {European Mathematical Society Publishing House},
title = {Slowdown estimates and central limit theorem for random walks in random environment},
url = {http://eudml.org/doc/277558},
volume = {002},
year = {2000},
}

TY - JOUR
AU - Sznitman, Alain-Sol
TI - Slowdown estimates and central limit theorem for random walks in random environment
JO - Journal of the European Mathematical Society
PY - 2000
PB - European Mathematical Society Publishing House
VL - 002
IS - 2
SP - 93
EP - 143
AB - 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 $\mathbb {Z}^d$, 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 previouswork of the author [24], concerning estimates of probabilities of slowdowns for walks which are neutral or biased to the right.
LA - eng
KW - multi-dimensional random walk; Kalikow’s condition; slowdown; trap; random walks in random environment; central limit theorem; large deviations
UR - http://eudml.org/doc/277558
ER -

Citations in EuDML Documents

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  1. Tomasz Komorowski, Grzegorz Krupa, The law of large numbers for ballistic, multi-dimensional random walks on random lattices with correlated sites
  2. Firas Rassoul-Agha, Timo Seppäläinen, Almost sure functional central limit theorem for ballistic random walk in random environment
  3. Martin P. W. Zerner, Velocity and Lyapounov exponents of some random walks in random environment
  4. Erwin Bolthausen, Alain-Sol Sznitman, Ofer Zeitouni, Cut points and diffusive random walks in random environment
  5. Atilla Yilmaz, Averaged large deviations for random walk in a random environment
  6. Lian Shen, On ballistic diffusions in random environment
  7. Francis Comets, Jeremy Quastel, Alejandro F. Ramírez, Fluctuations of the front in a stochastic combustion model
  8. Tom Schmitz, Diffusions in random environment and ballistic behavior

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