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Random walk in random scenery: A survey of some recent results

Frank den Hollander ; Jeffrey Steif (Institutionen för matematiska vetenskaper, matematik)
Stochastics and Dynamics (0219-4937). Vol. 48 (2006), p. 53-65.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Random walk in random scenery, K-automorphism, Bernoulli,weak Bernoulli, finitary coding, scenery reconstruction

Denna post skapades 2006-12-22. Senast ändrad 2014-09-29.
CPL Pubid: 24586


Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)


Annan matematik

Chalmers infrastruktur