论文标题
Gibbs措施
Gibbs measures on Subshifts
论文作者
论文摘要
数学物理学，概率，热力学形式主义，符号动力学等社区的许多研究人员都使用了吉布斯度量的概念。一个自然的问题是，吉布斯的这几个不同概念衡量一致。我们研究了$ d- $汇总变体的吉布斯措施的属性，该功能是在$ x $上定义的。根据Meyerovitch的工作，我们证明，如果$ x $是有限类型（SFT）的子缩影，那么任何平衡度量也是Gibbs度量。尽管Meyerovitch提供的定义并未提及条件期望，但我们表明，在$ x $是SFT的情况下，可以根据使用DLR方程的数学物理学文献中提出的更熟悉的概念来表征这些措施。
The notion of Gibbs Measure is used by many researchers of the communities of Mathematical Physics, Probability, Thermodynamic Formalism, Symbolic Dynamics, and others. A natural question is when these several different notions of Gibbs measure coincide. We study the properties of Gibbs measures for functions with $d-$summable variation defined on a subshift $X$. Based on Meyerovitch's work, we prove that if $X$ is a subshift of finite type (SFT), then any equilibrium measure is also a Gibbs measure. Although the definition provided by Meyerovitch does not make any mention to conditional expectations, we show that in the case where $X$ is a SFT, it is possible to characterize these measures in terms of more familiar notions presented in the literature of Mathematical Physics using DLR equations.
