一个完全随机的T-曲面模型和Gibbsian扩张
A completely random T-tessellation model and Gibbsian extensions
摘要：
Arak，Clifford和Surgailis在1993年的论文中讨论了随机可平面图的一个新模型.作为一种特殊情况，该模型产生仅具有T顶点的镶嵌（T镶嵌）。使用类似的方法，涉及泊松线，一个新的模型的随机T-镶嵌。将Campbell测度、Papangelou核和Georgii-Nguyen-Zessin公式从点过程理论转化为随机T-镶嵌。结果表明，新的模型表现出类似的泊松点过程的属性，因此可以被认为是一个完全随机的T-镶嵌。吉布斯变量引入导致随机T-镶嵌模型，其中选定的功能进行控制。吉布斯随机T-镶嵌被期望更好地表示观察到的镶嵌。由于数值实验是研究Gibbs模型的重要工具，我们推导了Metropolis-Hastings-Green族的模拟算法。
英文摘要：
In their 1993 paper, Arak, Clifford and Surgailis discussed a new model of random planar graph. As a particular case, that model yields tessellations with only T-vertices (T-tessellations). Using a similar approach involving Poisson lines, a new model of random T-tessellations is proposed. Campbell measures, Papangelou kernels and Georgii-Nguyen-Zessin formulae are translated from point process theory to random T-tessellations. It is shown that the new model shows properties similar to the Poisson point process and can therefore be considered as a completely random T-tessellation. Gibbs variants are introduced leading to models of random T-tessellations where selected features are controlled. Gibbs random T-tessellations are expected to better represent observed tessellations. As numerical experiments are a key tool for investigating Gibbs models, we derive a simulation algorithm of the Metropolis-Hastings-Green family.
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