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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
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