On random walks in random scenery

This paper considers 1-dimensional generalized random walks in random scenery. That is, the steps of the walk are generated by an arbitrary stationary process, and also the scenery is a priori arbitrary stationary. Under an ergodicity condition--which is satisfied in the classical case--a simple proof of the distinguishability of periodic sceneries is given.Comment: Published at http://dx.doi.org/10.1214/074921706000000068 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Scenery Reconstruction on Finite Abelian Groups

We consider the question of when a random walk on a finite abelian group with a given step distribution can be used to reconstruct a binary labeling of the elements of the group, up to a shift. Matzinger and Lember (2006) give a sufficient condition for reconstructibility on cycles. While, as we show, this condition is not in general necessary, our main result is that it is necessary when the length of the cycle is prime and larger than 5, and the step distribution has only rational probabilities. We extend this result to other abelian groups.Comment: 16 pages, 2 figure

Scenery reconstruction in two dimensions with many colors

Kesten has observed that the known reconstruction methods of random sceneries seem to strongly depend on the one-dimensional setting of the problem and asked whether a construction still is possible in two dimensions. In this paper we answer this question in the affirmative under the condition that the number of colors in the scenery is large enough

Mixing properties of the generalized T,T-1-process

Analysis and Stochastic