# Slowdown estimates for ballistic random walk in random environment

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 1, page 127-174
- ISSN: 1435-9855

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topBerger, 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 -

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