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Projections of Gibbs States for Hölder Potentials

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Abstract

We give a short proof that the projection of a Gibbs state for a Hölder continuous potential on a mixing shift of finite type under a 1-block fiber-wise mixing factor map has a Hölder continuous g function. This improves a number of previous results. The key insight in the proof is to realize the measure of a cylinder set in terms of positive operators and use cone techniques.

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Acknowledgements

I am grateful to Anthony Quas and Chris Bose for many useful discussions, as well as careful readings and helpful suggestions on several drafts of this manuscript. I am also grateful for suggestions by the referees which helped improve the exposition.

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  1. University of Victoria, PO Box 1700 STN CSC, Victoria, BC, V8W 2Y2, Canada

    Mark Piraino

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  1. Mark Piraino
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Correspondence to Mark Piraino.

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Piraino, M. Projections of Gibbs States for Hölder Potentials. J Stat Phys 170, 952–961 (2018). https://doi.org/10.1007/s10955-018-1967-3

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  • DOI: https://doi.org/10.1007/s10955-018-1967-3

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