Random walks in random environments without ellipticity

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Lenci, Marco^1,2 

[1] Univ Bologna, Dipartmento Matemat, I-40126 Bologna, Italy

[2] Ist Nazl Fis Nucl, Sez Bologna, I-40126 Bologna, Italy

关键词: RWRE;    Ellipticity;    Partial transitivity;    Ergodicity;    Point of view of the particle;    Doubly stochastic environments;    Martingales;    Quenched Invariance Principle;   

DOI  :  10.1016/j.spa.2013.01.007

来源: Elsevier

【 摘 要 】

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. 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). (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free