Heil, Hadrian A stationary, mixing and perturbative counterexample to the 0-1-law for random walk in random environment in two dimensions. (English) Zbl 1286.60101 Electron. J. Probab. 18, Paper No. 1, 33 p. (2013). Summary: We construct a two-dimensional counterexample of a random walk in random environment (RWRE). The environment is stationary, mixing and \(\varepsilon\)-perturbative, and the corresponding RWRE has non-trivial probability to wander off to the upper right. This is in contrast to the 0-1-law that holds for i.i.d. environments. Cited in 1 Document MSC: 60K37 Processes in random environments 60F20 Zero-one laws Keywords:random walk in random environment; 0-1-law; counterexample PDF BibTeX XML Cite \textit{H. Heil}, Electron. J. Probab. 18, Paper No. 1, 33 p. (2013; Zbl 1286.60101) Full Text: DOI arXiv