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Nonuniqueness ing-functions

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Abstract

We give an example of two distinct stationary processes {X n} and {X′ n} on {0, 1} for whichP[X0=1|X−1=a−1,X−2=a−2, …]=P[X′0=1|X′−1=a−1,X′−2=a−2, …] for all {a i},i=−1, −2, …, even though these probabilities are bounded away from 0 and 1, and are continuous in {a i}.

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References

  1. M. Aizenman, J. Chayes, L. Chayes and C. Newman,Discontinuity of the magnetization in one-dimensional 1/|x−y| 2 Ising and Potts models, J. Stat. Physics50 (1988), 1–40.

    Article  MATH  MathSciNet  Google Scholar 

  2. H. Berbee,Chains with infinite connections: uniqueness and Markov representation, Probability Theory and Related Fields76 (1987), 243–253.

    Article  MATH  MathSciNet  Google Scholar 

  3. W. Doeblin and R. Fortet,Sur les chaines a liaisons completes, Bull. Soc. Math. Fr.65 (1937), 132–148.

    MATH  MathSciNet  Google Scholar 

  4. T. Harris,On chains of infinite order, Pacific Journal Math.5 (1955), 707–724.

    MATH  Google Scholar 

  5. S. Kalikow,Random Markov processes and uniform martingales, Israel Journal of Mathematics71 (1990), 33–54.

    MATH  MathSciNet  Google Scholar 

  6. S. Kalikow, Y. Katznelson and B. Weiss,Finitarily deterministic generators for zero entropy systems, Israel J. Math.79, (1992), 33–45.

    MATH  MathSciNet  Google Scholar 

  7. M. Keane,Strongly mixing g-measures, Invent. Math.16, (1972), 309–324.

    Article  MATH  MathSciNet  Google Scholar 

  8. B. Petit,Schemas de Bernoulli et g-mesures, C. R. Acad. Sci. Paris, Ser. A280 (1975), 17–20.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA

    Maury Bramson

  2. Mathematical Sciences Institute, Cornell University, 14853, Ithaca, NY, USA

    Steven Kalikow

Authors
  1. Maury Bramson
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  2. Steven Kalikow
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Additional information

Supported in part by NSF Grant DMS 89-01545.

Supported in part by the US Army Research Office.

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Bramson, M., Kalikow, S. Nonuniqueness ing-functions. Israel J. Math. 84, 153–160 (1993). https://doi.org/10.1007/BF02761697

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  • DOI: https://doi.org/10.1007/BF02761697

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