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The positive-divergence and blowing-up properties

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Abstract

A property of ergodic finite-alphabet processes, called the blowing-up property, is shown to imply exponential rates of convergence for frequencies and entropy, which in turn imply a positive-divergence property. Furthermore, processes with the blowing-up property-divergence property. Furthermore, processes with the blowing-up property are finitely determined and the finitely determined property plus exponential rates of convergence for frequencies and for entropy implies blowing-up. It is also shown that finitary codings of i.i.d. processes have the blowing-up property.

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Authors and Affiliations

  1. Mathematics Institute, Hungarian Academy of Sciences, Hungary

    Katalin Marton

  2. University of Toledo and Eötvös Loránd University, USA

    Paul C. Shields

Authors
  1. Katalin Marton
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  2. Paul C. Shields
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Additional information

Partially supported by Hungarian National Foundation for Scientific Research Grant OTKA 1906.

Partially supported by NSF grant DMS-9024240.

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Marton, K., Shields, P.C. The positive-divergence and blowing-up properties. Israel J. Math. 86, 331–348 (1994). https://doi.org/10.1007/BF02773685

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  • DOI: https://doi.org/10.1007/BF02773685

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