# The Lanford-Ruelle theorem for actions of sofic groups

@inproceedings{Barbieri2021TheLT, title={The Lanford-Ruelle theorem for actions of sofic groups}, author={Sebastiano Barbieri and Tom Meyerovitch}, year={2021} }

Let Γ be a sofic group, Σ be a sofic approximation sequence of Γ and X be a Γ-subshift with nonnegative sofic topological entropy with respect to Σ. Further assume that X is a shift of finite type, or more generally, that X satisfies the topological Markov property. We show that for any sufficiently regular potential f : X → R, any translation-invariant Borel probability measure on X which maximizes the measure-theoretic sofic pressure of f with respect to Σ, is a Gibbs state with respect to f…

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