Random walk in random scenery.

Abstract: In this talk we address the question: ``What do you see when you randomly move through a random landscape?''. Specifically, we consider the example of a random walk on the d-dimensional integer lattice whose sites are colored black or white in some random fashion. We look at the sequence of colors the walk encounters on its way (the ``color record''). We show that this random sequence has some remarkable ergodic properties, depending on the dimension d and on the way in which the lattice is randomly colored.