## The Annals of Probability

### 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+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.

#### Article information

Source
Ann. Probab., Volume 35, Number 1 (2007), 1-31.

Dates
First available in Project Euclid: 19 March 2007

https://projecteuclid.org/euclid.aop/1174324122

Digital Object Identifier
doi:10.1214/009117906000000610

Mathematical Reviews number (MathSciNet)
MR2303942

Zentralblatt MATH identifier
1126.60090

#### Citation

Rassoul-Agha, Firas; Seppäläinen, Timo. Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction. Ann. Probab. 35 (2007), no. 1, 1--31. doi:10.1214/009117906000000610. https://projecteuclid.org/euclid.aop/1174324122

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