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10. Random walk on random walks

Author

Hilário, Marcelo, primary, den Hollander, Frank, additional, Sidoravicius, Vladas, additional, Soares dos Santos, Renato, additional, and Teixeira, Augusto, additional

Published
2015
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11. Random walk in random scenery: A survey of some recent results

Author

den Hollander, Frank and Steif, Jeffrey E.

Subjects
K-automorphism, conditional probability distribution, Bernoulli, 82B20, random walk in random scenery, Computer Science::Human-Computer Interaction, bad configuration, Computer Science::Robotics, Computer Science::Graphics, Mathematics::Probability, finitary coding, scenery reconstruction, 60G10, weak Bernoulli
Abstract

In this paper we give a survey of some recent results for random walk in random scenery (RWRS). On $\Z^d$, $d\geq 1$, we are given a random walk with i.i.d. increments and a random scenery with i.i.d. components. The walk and the scenery are assumed to be independent. RWRS is the random process where time is indexed by $\Z$, and at each unit of time both the step taken by the walk and the scenery value at the site that is visited are registered. We collect various results that classify the ergodic behavior of RWRS in terms of the characteristics of the underlying random walk (and discuss extensions to stationary walk increments and stationary scenery components as well). We describe a number of results for scenery reconstruction and close by listing some open questions.

Published
2006

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