平面一致多边形马氏场高阶相关函数的多边形网表示
Polygonal web representation for higher order correlation functions of consistent polygonal Markov fields in the plane
摘要：
本文考虑由Arak和Surgailis（1982，1989）提出的多边形马尔可夫场.我们的注意力集中在领域与节点的顺序2，这可以被视为连续集成的不相交的轮廓在平面上，共享一些显着的特点与二维伊辛模型。本文的目的是建立一个显式的随机表示的高阶相关函数的多边形马尔可夫场在其一致性制度。该表示是在所谓的作物功能（定义由莫比乌斯型公式）的多边形网络出现在一个图形建设的双重，从而产生多边形领域。通过构造多边形域的相关函数与多边形网的裁剪泛函之间的鞅插值来证明我们的表示公式。
英文摘要：
We consider polygonal Markov fields originally introduced by Arak and Surgailis (1982,1989). Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane, sharing a number of salient features with the two-dimensional Ising model. The purpose of this paper is to establish an explicit stochastic representation for the higher-order correlation functions of polygonal Markov fields in their consistency regime. The representation is given in terms of the so-called crop functionals (defined by a Moebius-type formula) of polygonal webs which arise in a graphical construction dual to that giving rise to polygonal fields. The proof of our representation formula goes by constructing a martingale interpolation between the correlation functions of polygonal fields and crop functionals of polygonal webs.
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