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Quenched exit estimates and ballisticity conditions for higher-dimensional random walk in random environment

2012
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Annals of Probability
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Consider a random walk in an i.i.d. uniformly elliptic environment in dimensions larger than one. In 2002, Sznitman introduced for each $\gamma\in(0,1)$ the ballisticity condition $(T)_{\gamma}$ and the condition $(T')$ defined as the fulfillment of $(T)_{\gamma}$ for each $\gamma\in(0,1)$. Sznitman proved that $(T')$ implies a ballistic law of large numbers. Furthermore, he showed that for all $\gamma\in (0.5,1)$, $(T)_{\gamma}$ is equivalent to $(T')$. Recently, Berger has proved that in

doi:10.1214/10-aop637
fatcat:6h6zpo2cs5gpper7cjcipvjmhi