More Randomness of Environment Does Not Always Slow Down a Random Walk

Christiane Takacs ()
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Christiane Takacs: Universität Linz

Journal of Theoretical Probability, 2001, vol. 14, issue 3, 699-715

Abstract: Abstract 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.

Keywords: random walk; random environment; entropy; speed (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1017593006635

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