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

Details Reconstructing a two-color scenery by observing it along a simple random walk path Reconstructing a two-color scenery by observing it along a simple random walk path

2005-03-24

arxiv.org/abs/math/0503517v1

Annals of Applied Probability 2005, Vol. 15, No. 1B, 778-819

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000972 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000972

Let {\xi (n)}_{n\in Z} be a two-color random scenery, that is, a random coloring of Z in two colors, such that the \xi (i)'s are i.i.d. Bernoulli variables with parameter \tfrac12. Let {S(n)}_{n\in N} be a symmetric random walk starting at 0. Our main result shows that a.s., \xi \circ S (the composition of \xi and S) determines \xi up to translation and reflection. In other words, by observing the scenery \xi along the random walk path S, we can a.s. reconstruct \xi up to translation and reflection. This result gives a positive answer to the question of H. Kesten of whether one can a.s. detect a single defect in almost every two-color random scenery by observing it only along a random walk path.

Affiliated with

Also associated with

No associations

Rating

Reconstructing a two-color scenery by observing it along a simple random walk path does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Reconstructing a two-color scenery by observing it along a simple random walk path, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reconstructing a two-color scenery by observing it along a simple random walk path will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-586884