Random walk in random scenery: A survey of some recent results
Journal article, 2006
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.
Random walk in random scenery