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

Abstract

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.

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

References in corpus (3)

• An almost sure invariance principle for random walks in a space-time random environment
• The random average process and random walk in a space-time random environment in one dimension
• Ballistic Random Walk in a Random Environment with a Forbidden Direction

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