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VOL. 48 | 2006 Random walk in random scenery: A survey of some recent results
Jeffrey E. Steif, Frank den Hollander

Editor(s) Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy

## 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.

## Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1124.60084
MathSciNet: MR2306188

Digital Object Identifier: 10.1214/074921706000000077

Subjects:
Primary: 60G10
Secondary: 82B20