TY - JOUR

T1 - Reconstructing a three-color scenery by observing it along a simple random walk path

AU - Matzinger, H.

PY - 1999

Y1 - 1999

N2 - Let {¿(n)}n¿Z be a three-color random scenery, i.e., a random coloration of Z in three colors, such that the colors of the different points in N are i.i.d. Let {S(n)}n¿N be a symmetric random walk starting at 0. Our main result shows that a.s., ¿°S (the composition of ¿ and S) determines ¿ up to translation and reflection. In other words, by observing the scenery along the random walk path S, we can a.s. reconstruct ¿ up to translation and reflection. This result allows us to give a positive answer to the question of H. Kesten of whether one can a.s. detect a single defect in a three-color random scenery by observing it only along a random walk path.

AB - Let {¿(n)}n¿Z be a three-color random scenery, i.e., a random coloration of Z in three colors, such that the colors of the different points in N are i.i.d. Let {S(n)}n¿N be a symmetric random walk starting at 0. Our main result shows that a.s., ¿°S (the composition of ¿ and S) determines ¿ up to translation and reflection. In other words, by observing the scenery along the random walk path S, we can a.s. reconstruct ¿ up to translation and reflection. This result allows us to give a positive answer to the question of H. Kesten of whether one can a.s. detect a single defect in a three-color random scenery by observing it only along a random walk path.

U2 - 10.1002/(SICI)1098-2418(199909)15:2<196::AID-RSA5>3.0.CO;2-#

DO - 10.1002/(SICI)1098-2418(199909)15:2<196::AID-RSA5>3.0.CO;2-#

M3 - Article

VL - 15

SP - 196

EP - 207

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

SN - 1042-9832

IS - 2

ER -