(1) Mathematics Department, Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, USA;(2) Mathematics Department, University of Wisconsin-Madison, Van Vleck Hall, Madison, WI 53706, USA
Abstract:
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 L2 averaged 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.
T. Sepp?l?inen was partially supported by National Science Foundation grant DMS-0402231.