Thinking of a deterministic function s : Z+ N as "scenery" on the integers, a random walk (Z,,, Z,, Z , , . . .) on Z generates a random record of scenery ''observed'' along the walk: s ( Z ) = (s(Z,), s(Z,), . . .). Suppose t : Z + N is another scenery on the integers that is neither a translate of
Distinguishing certain random sceneries on ##Z## via random walks
โ Scribed by C.Douglas Howard
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 476 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
โฆ Synopsis
We prove a fixed versus random scenery distinguishability result (along the lines of Benjamini and Kesten) for 0-1 valued scenery on ~_ where the distances between successive l's in the random scenery are i.i.d, random variables with fat tails. This result is an application of a more general strategy for establishing fixed/random distinguishability.
๐ SIMILAR VOLUMES
For any 1 1 measure-preserving map T of a probability space, consider the [T, T &1 ] endomorphism and the corresponding decreasing sequence of \_-algebras. We demonstrate that if the decreasing sequence of \_-algebras generated by [T, T &1 ] and [S, S &1 ] are isomorphic, then T and S must have equa