Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction
Firas Rassoul-Agha and Timo Seppäläinen
Source: Ann. Probab. Volume 35, Number 1 (2007), 1-31.
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+ɛ 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.
Primary Subjects: 60K37, 60F17, 82D30
Keywords: Random walk in random environment; point of view of particle; renewal; invariant measure; invariance principle; functional central limit theorem
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1174324122
Digital Object Identifier: doi:10.1214/009117906000000610
Zentralblatt MATH identifier:
1126.60090
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