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Entropy and Dyadic Equivalence of Random Walks on a Random Scenery

✍ Scribed by Deborah Heicklen; Christopher Hoffman; Daniel J. Rudolph

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 192 KB
Volume: 156
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.2000.1940

No coin nor oath required. For personal study only.

✦ Synopsis

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 equal entropies. As a consequence, if the [T, T &1 ] endomorphism is isomorphic to the [S, S &1 ] endomorphism, then the entropy of T is equal to the entropy of S. Central to this is a relationship between Feldman's f metric (1976,

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