Reconstructing a 2-color scenery by observing it along a simple random walk path
نویسندگان
چکیده
Let {~(n)}nEZbe a 2-color random scenery, that is a random coloration of in two colors, such that the ~(i)'s are i.i.d. Bernoulli variables with parameter~. Let {S(n)}nEN be a symmetric random walk starting at O. Our main result shows that a.s., ~ 0 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 almost any 2-color random scenery by observing it only along a
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Reconstructing a three-color scenery by observing it along a simple random walk path
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