Slowdown estimates for ballistic random walk in random environment

Berger, Noam. "Slowdown estimates for ballistic random walk in random environment." Journal of the European Mathematical Society 014.1 (2012): 127-174. <http://eudml.org/doc/277559>.

@article{Berger2012,
abstract = {We consider models of random walk in uniformly elliptic i.i.d. random environment in dimension greater than or equal to 4, satisfying a condition slightly weaker than the ballisticity condition $(T^\{\prime \})$. We show that for every $\epsilon > 0$ and $n$ large enough, the annealed probability of linear slowdown is bounded from above by $\exp (-(\log n)^\{d-\epsilon \})$. This bound almost matches the known lower bound of $\exp (-C(\log n)^d)$, and significantly improves previously known upper bounds. As a corollary we provide almost sharp estimates for the quenched probability of slowdown. As a tool for obtaining the main result, we show an almost local version of the quenched central limit theorem under the assumption of the same condition.},
author = {Berger, Noam},
journal = {Journal of the European Mathematical Society},
keywords = {random walk; random environment; ballisticity; plain nestling; slowdown estimates; random walk; random environment; ballisticity; plain nestling; slowdown estimates},
language = {eng},
number = {1},
pages = {127-174},
publisher = {European Mathematical Society Publishing House},
title = {Slowdown estimates for ballistic random walk in random environment},
url = {http://eudml.org/doc/277559},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Berger, Noam
TI - Slowdown estimates for ballistic random walk in random environment
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 1
SP - 127
EP - 174
AB - We consider models of random walk in uniformly elliptic i.i.d. random environment in dimension greater than or equal to 4, satisfying a condition slightly weaker than the ballisticity condition $(T^{\prime })$. We show that for every $\epsilon > 0$ and $n$ large enough, the annealed probability of linear slowdown is bounded from above by $\exp (-(\log n)^{d-\epsilon })$. This bound almost matches the known lower bound of $\exp (-C(\log n)^d)$, and significantly improves previously known upper bounds. As a corollary we provide almost sharp estimates for the quenched probability of slowdown. As a tool for obtaining the main result, we show an almost local version of the quenched central limit theorem under the assumption of the same condition.
LA - eng
KW - random walk; random environment; ballisticity; plain nestling; slowdown estimates; random walk; random environment; ballisticity; plain nestling; slowdown estimates
UR - http://eudml.org/doc/277559
ER -