Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction

Details Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction

2007-03-27

arxiv.org/abs/math/0703787v1

Annals of Probability 2007, Vol. 35, No. 1, 1-31

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000610 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000610

We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The assumptions are nonnestling, at least two spatial dimensions, and a $2+\epsilon$ moment for the step of the walk uniformly in the environment. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.

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