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Projection of Markov Measures May Be Gibbsian

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Abstract

We study the induced measure obtained from a 1-step Markov measure, supported by a topological Markov chain, after the mapping of the original alphabet onto another one. We give sufficient conditions for the induced measure to be a Gibbs measure (in the sense of Bowen) when the factor system is again a topological Markov chain. This amounts to constructing, when it does exist, the induced potential and proving its Hölder continuity. This is achieved through a matrix method. We provide examples and counterexamples to illustrate our results.

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Authors and Affiliations

  1. CPHT-CNRS, École Polytechnique, 91128, Palaiseau Cedex, France

    J.-R. Chazottes

  2. IICO-UASLP, A. Obregón 64, 78000, San Luis Potosí, SLP, México

    E. Ugalde

Authors
  1. J.-R. Chazottes
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  2. E. Ugalde
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Chazottes, JR., Ugalde, E. Projection of Markov Measures May Be Gibbsian. Journal of Statistical Physics 111, 1245–1272 (2003). https://doi.org/10.1023/A:1023056317067

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