Asymptotic properties of certain anisotropic walks in random media (Q1872396)

A class of anisotropic random walks in random media on \(Z^d\) is studied. These random walks have reversible Markov chains when the environment is fixed, but for which the chain of the environment viewed from the particle has no obvious invariant measure absolutely continuous to the static measure. The goal of the paper is to derive a strong law of large numbers with nonvanishing limiting velocity and a functional central limit theorem for the anisotropic random motion in random environment under consideration. The approach of the paper 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 \textit{A.-S. Sznitman} and \textit{M. Zerner} [Ann. Probab. 27, 1851-1869 (1999; Zbl 0965.60100)]. With the help of these times an ergodic Markov structure is considered.