Ballistic Random Walk in a Random Environment with a Forbidden Direction

Details Ballistic Random Walk in a Random Environment with a Forbidden Direction Ballistic Random Walk in a Random Environment with a Forbidden Direction

2005-10-18

arxiv.org/abs/math/0510392v1

ALEA Lat. Am. J. Probab. Math. Stat. 1 (2006), 111--147 (electronic)

Mathematics

Probability

Scientific paper

We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. Homogenization and regeneration techniques combine to prove a law of large numbers and an averaged invariance principle. The assumptions are non-nestling and $1+\e$ (resp.\ $2+\e$) moments for the step of the walk uniformly in the environment, for the law of large numbers (resp. invariance principles). We also investigate invariance principles under fixed environments, and invariance principles for the environment-dependent mean of the walk.

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