Indistinguishable Sceneries

In this paper we give a counterexample to a conjecture mentioned in Benw Ž .x jamini and Kesten J. d’Anal. Math., 69, 97]135 1996 about distinguishing sceneries by observing them along a simple random walk, giving an explicit construction of 2/0 sceneries that are all pairwise indistinguishable. Q 1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 71]86, 1999