The Annals of Probability

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

Firas Rassoul-Agha and Timo Seppäläinen

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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

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

First available in Project Euclid: 19 March 2007

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Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments 60F17: Functional limit theorems; invariance principles 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

Random walk in random environment point of view of particle renewal invariant measure invariance principle functional central limit theorem


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.

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