Asymptotic properties of certain anisotropic walks in random media

Abstract

We discuss a class of anisotropic random walks in a random media on$\mathbb{Z}^{d}$, $d\geq1$, which have reversible transition kernels when the environment is fixed. The aim is to derive a strong law of large numbers and a functional central limit theorem for this class of models. The technique of the environment viewed from the particle does not seem to apply well in this setting. Our approach is based on the technique of introducing certain times similar to the regeneration times in the work concerning random walks in i.i.d. random environment by Sznitman and Zerner. With the help of these times we are able to construct anergodic Markov structure.