Marco Lenci. Random walks in random environments without ellipticity

Natural Sciences / Mathematics / Probability

Submitted on: May 11, 2012, 20:30:47

Description: 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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