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arXiv · 2209.13291

Uniqueness and statistical properties of the Gibbs state on general one-dimensional lattice systems with markovian structure

Victor Vargas
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Abstract

Let $M$ be a compact metric space and $X = M^{\mathbb{N}}$, we consider a set of admissible sequences $X_{A, I} \subset X$ determined by a continuous admissibility function $A : M \times M \to \mathbb{R}$ and a compact set $I \subset \mathbb{R}$. Given a Lipschitz continuous potential $\varphi : X_{A, I} \to \mathbb{R}$, we prove uniqueness of the Gibbs state $\mu_\varphi$ and we show that it is a Gibbs-Bowen measure and satisfies a central limit theorem.

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Victor Vargas. 2022-09-27. Uniqueness and statistical properties of the Gibbs state on general one-dimensional lattice systems with markovian structure. https://doi.org/10.1142/s0219493723500387

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