论文标题
关于吉布斯（Gibbs
A Note on the Existence of Gibbs Marked Point Processes with Applications in Stochastic Geometry
论文作者
论文摘要
本文概括了无限量标记的吉布斯点过程的最新存在结果。我们尝试将存在定理用于从随机几何形状中的两个模型。首先，我们在$ \ mathbb {r}^d $中显示了Gibbs Facet过程的存在，并具有排斥性交互。我们还证明，具有有吸引力相互作用的有限体积吉布斯刻画工艺不必存在。之后，我们研究了$ \ mathbb {r}^2 $的gibbs-laguerre tessellations。上述存在结果无法使用，因为它的假设之一不满意，但是我们能够显示出具有特定能量函数的无限量gibbs-laguerre工艺的存在，这是在我们几乎肯定会看到一个点的假设下。
This paper generalizes a recent existence result for infinite-volume marked Gibbs point processes. We try to use the existence theorem for two models from stochastic geometry. First, we show the existence of Gibbs facet processes in $\mathbb{R}^d$ with repulsive interactions. We also prove that the finite-volume Gibbs facet processes with attractive interactions need not exist. Afterwards, we study Gibbs-Laguerre tessellations of $\mathbb{R}^2$. The mentioned existence result cannot be used, since one of its assumptions is not satisfied for tessellations, but we are able to show the existence of an infinite-volume Gibbs-Laguerre process with a particular energy function, under the assumption that we almost surely see a point.
