An almost sure invariance principle for random walks in a space-time random environment

Details An almost sure invariance principle for random walks in a space-time random environment An almost sure invariance principle for random walks in a space-time random environment

2004-11-26

arxiv.org/abs/math/0411602v1

Probab. Th. Rel. Fields, 133(3), 299 - 314 (2005)

Mathematics

Probability

Scientific paper

10.1007/s00440-004-0424-1

We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance principle and considering environments with an annealed $L^2$ drift. We also state an a.s. invariance principle for random walks in general random environments whose hypothesis requires a subdiffusive bound on the variance of the quenched mean, under an ergodic invariant measure for the environment chain.

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