On the Critical Dimension and AC Entropy for Markov Odometers |
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Authors: | A. H. Dooley G. Mortiss |
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Affiliation: | (1) University of New South Wales, Sydney, Australia |
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Abstract: | Markov odometers are natural models for non-homogeneous Markov chains, and are natural generalisations of infinite product measures. We show how to calculate the critical dimension of these measures: this is an invariant which describes the asymptotic growth rate of sums of Radon-Nikodym derivatives. This interesting invariant appears to give a kind of entropy for non-singular odometer actions. The techniques require a law of large numbers for inhomogeneous Markov chains. |
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Keywords: | 2000 Mathematics Subject Classification: 28D99 28D20 |
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