Geodesic
Slowdown estimates for ballistic random walk in random environment
Journal of the European Mathematical Society, Tome 14 (2012) no. 1, pp. 127-174

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DOI

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′). We show that for every ε>0 and n large enough, the annealed probability of linear slowdown is bounded from above by exp(−(logn)d−ε). This bound almost matches the known lower bound of exp(−C(logn)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.
DOI : 10.4171/jems/298
Classification : 60-XX, 00-XX 
Noam Berger. Slowdown estimates for ballistic random walk in random environment. Journal of the European Mathematical Society, Tome 14 (2012) no. 1, pp. 127-174. doi: 10.4171/jems/298
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     author = {Noam Berger},
     title = {Slowdown estimates for ballistic random walk in random environment},
     journal = {Journal of the European Mathematical Society},
     pages = {127--174},
     year = {2012},
     volume = {14},
     number = {1},
     doi = {10.4171/jems/298},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/298/}
}
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