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 $A:M\times M\to ℝ$ and a compact set $I\subset ℝ$. Given a Lipschitz continuous potential $\phi :X_{A,I}\to ℝ$, we prove uniqueness of the Gibbs state ${\mu }_{\phi }$ and we show that it is a Gibbs–Bowen measure and satisfies a central limit theorem.

中文翻译：

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马尔可夫结构的一般一维晶格系统吉布斯态的唯一性和统计性质

让$\mathrm{中号}$是一个紧度量空间并且$X={\mathrm{中号}}^{\mathbb{N}}$，我们考虑一组可接受的序列$X_{A,我}\subset X$由连续容许函数确定$A:\mathrm{中号}\times \mathrm{中号}\to ℝ$和一个紧凑的集合$我\subset ℝ$。考虑到利普希茨的连续潜力$\phi :X_{A,我}\to ℝ$，我们证明吉布斯状态的唯一性${\mu }_{\phi }$我们证明它是吉布斯-鲍文测度并且满足中心极限定理。