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arXiv · 2308.16641

Gibbs Measures on Multidimensional Spaces. Equivalences and a Groupoid Approach

Rodrigo Bissacot·Bruno Hideki Fukushima-Kimura·Rafael Pereira Lima·Thiago Raszeja
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Abstract

We consider some of the main notions of Gibbs measures on subshifts introduced by different communities, such as dynamical systems, probability, operator algebras, and mathematical physics. For potentials with $d$-summable variation, we prove that several of the definitions considered by these communities are equivalent. In particular, when the subshift is of finite type (SFT), we show that all definitions coincide. In addition, we introduced a groupoid approach to describe some Gibbs measures, allowing us to show the equivalence between Gibbs measures and KMS states (the quantum analogous to the Gibbs measures).

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Rodrigo Bissacot, Bruno Hideki Fukushima-Kimura, Rafael Pereira Lima, Thiago Raszeja. 2023-08-31. Gibbs Measures on Multidimensional Spaces. Equivalences and a Groupoid Approach. https://arxiv.org/abs/2308.16641

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