Takacs, Christiane More randomness of environment does not always slow down a random walk. (English) Zbl 0989.60046 J. Theor. Probab. 14, No. 3, 699-715 (2001). Summary: We consider a random walk on \(\mathbb{Z}\) in a stationary and ergodic random environment, whose states are called types of the vertices of \(\mathbb{Z}\). We find conditions for which the speed of the random walk is positive. In the case of a Markov chain environment with finitely many states, we give an explicit formula for the speed and for the asymptotic proportion of time spent at vertices of a certain type. Using these results, we compare the speed of random walks on \(\mathbb{Z}\) in environments of varying randomness. MSC: 60G50 Sums of independent random variables; random walks 60K37 Processes in random environments Keywords:random walk; random environment; entropy; speed PDF BibTeX XML Cite \textit{C. Takacs}, J. Theor. Probab. 14, No. 3, 699--715 (2001; Zbl 0989.60046) Full Text: DOI