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arXiv · 2007.05862

A Dobrushin-Lanford-Ruelle theorem for irreducible sofic shifts

Luísa Borsato·Sophie MacDonald
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Abstract

We show that for a potential with summable variations on an irreducible sofic shift in one dimension, the equilibrium measures are precisely the shift-invariant Gibbs measures. The main tool in the proof is a preservation of Gibbsianness result for almost invertible factor codes on irreducible shifts of finite type, which we then extend to finite-to-one codes by applying the results about equilibrium measures.

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Luísa Borsato, Sophie MacDonald. 2020-07-11. A Dobrushin-Lanford-Ruelle theorem for irreducible sofic shifts. https://arxiv.org/abs/2007.05862

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