Entropy and<Emphasis Type="Italic">σ</Emphasis>-algebra equivalence of certain random walks on random sceneries |
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Authors: | Karen Ball |
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Institution: | (1) Department of Mathematics, University of Maryland, College Park, 20742 College Park, MD, USA |
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Abstract: | LetX=X
0,X
1,…be a stationary sequence of random variables defining a sequence space Σ with shift mapσ and let (T
t, Ω) be an ergodic flow. Then the endomorphismT
X(x, ω)=(σ(x),T
x
0(ω)) is known as a random walk on a random scenery. In 4], Heicklen, Hoffman and Rudolph proved that within the class of random
walks on random sceneries whereX is an i.i.d. sequence of Bernoulli-(1/2, 1/2) random variables, the entropy ofT
t is an isomorphism invariant. This paper extends this result to a more general class of random walks, which proves the existence
of an uncountable family of smooth maps on a single manifold, no two of which are measurably isomorphic.
This research was sustained in part by fellowship support from the National Physical Science Consortium and the National Security
Agency. |
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Keywords: | |
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