Random walks in random environments without ellipticity

Details Random walks in random environments without ellipticity Random walks in random environments without ellipticity

2011-06-29

arxiv.org/abs/1106.6008v1

Mathematics

Probability

18 pages

Scientific paper

We consider random walks in random environments on Z^d. Under a transitivity hypothesis that is much weaker than the customary ellipticity condition, and assuming an absolutely continuous invariant measure on the space of the environments, we prove the ergodicity of the annealed process w.r.t. the dynamics "from the point of view of the particle". This implies in particular that the environment viewed from the particle is ergodic. An immediate application of this result is to bistochastic environments. In this case, assuming zero local drift as well (martingale condition), we also prove the quenched Invariance Principle.

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