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Finitary isomorphisms of some infinite entropy Bernoulli flows

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Abstract

A consequence of Ornstein theory is that the infinite entropy flows associated with Poisson processes and continuous-time irreducible Markov chains on a finite number of states are isomorphic as measure-preserving systems. We give an elementary construction of such an isomorphism that has an additional finitariness property, subject to the additional conditions that the Markov chain has a uniform holding rate and a mixing skeleton.

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Acknowledgements

I thank Zemer Kosloff and Amanda Wilkens for their helpful conversations. I also thank the referee for carefully reviewing this article and providing insightful suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics, University of Kansas, 405 Snow Hall, 1460 Jayhawk Blvd, Lawrence, Kansas, 66045-7594, USA

    Terry Soo

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  1. Terry Soo
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Correspondence to Terry Soo.

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Funded in part by a General Research Fund.

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Soo, T. Finitary isomorphisms of some infinite entropy Bernoulli flows. Isr. J. Math. 232, 883–897 (2019). https://doi.org/10.1007/s11856-019-1890-6

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  • DOI: https://doi.org/10.1007/s11856-019-1890-6

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