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arXiv · 2103.04467

Metastability and maximal-entropy joinings of Gibbs measures on finitely-generated groups

Christopher Shriver
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Abstract

We prove a metastability result for finitary microstates which are good models for a Gibbs measure for a nearest-neighbor interaction on a finitely-generated group. This is used to show that any maximal-entropy joining of two such Gibbs states is a relative product over the tail $\sigma$-algebra, except in degenerate cases. We also use results on extremal cuts of random graphs to further investigate optimal self-joinings of the Ising model on a free group.

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BibTeXRIS

Christopher Shriver. 2021-03-07. Metastability and maximal-entropy joinings of Gibbs measures on finitely-generated groups. https://arxiv.org/abs/2103.04467

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