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

Takacs, Christiane

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