论文标题
关于有限分布及其吉布斯形式的有限随机场的表征
On the characterization of a finite random field by conditional distribution and its Gibbs form
论文作者
论文摘要
在本文中，我们表明数学统计物理学的方法可以成功应用于有限体积的随机字段。结果，我们获得了具有一个分布的给定系统的有限随机场的存在和独特性的简单必要条件和唯一性。使用哈密顿量的公理（没有潜在的概念）定义，我们表明任何有限的随机场都是Gibbsian。我们还将提出的方法应用于马尔可夫随机字段。
In this paper, we show that the methods of mathematical statistical physics can be successfully applied to random fields in finite volumes. As a result, we obtain simple necessary and sufficient conditions for the existence and uniqueness of a finite random field with a given system of one-point conditional distributions. Using the axiomatic (without the notion of potential) definition of Hamiltonian, we show that any finite random field is Gibbsian. We also apply the proposed approach to Markov random fields.
