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More randomness of environment does not always slow down a random walk. (English) Zbl 0989.60046
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
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