Random walks in random environments without ellipticity

Marco Lenci

Stochastic Processes and their Applications, 2013, vol. 123, issue 5, 1750-1764

Abstract: We consider random walks in random environments on Zd. 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. As an example of application of this result, we give a general form of the quenched Invariance Principle for walks in doubly stochastic environments with zero local drift (martingale condition).

Keywords: RWRE; Ellipticity; Partial transitivity; Ergodicity; Point of view of the particle; Doubly stochastic environments; Martingales; Quenched Invariance Principle (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spa.2013.01.007

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