随机拉盖尔镶嵌的混合性质
Mixing Properties of Random Laguerre Tessellations
AI总结：
本文研究随机拉盖尔镶嵌的混合性质，推导其有良好定义的近最优充分条件，探究生成标记点过程的混合性质在该镶嵌中的保留情况，所用方法结合了标准逼近论证、tempered构型性质及拉盖尔映射可测性。
AI中文摘要：
本文研究由一般平稳标记点过程生成的随机拉盖尔镶嵌，它是沃罗诺伊镶嵌的加权推广。我们利用 tempered 构型（ tempered 配置）的概念处理可能无界的权重，首先推导生成标记点过程的近最优充分条件，以确保所得随机拉盖尔镶嵌有良好定义。随后，我们探究生成标记点过程的三种混合性质——遍历性、混合性和 α-混合性——如何在对应的随机拉盖尔镶嵌中保留。我们的方法结合了标准逼近论证、 tempered 构型的性质以及拉盖尔映射的可测性。
英文摘要：
In this paper, we study the random Laguerre tessellation, a weighted generalization of the Voronoi tessellation, generated by a general stationary marked point process. We first derive a nearly optimal sufficient condition on the generating marked point process which ensures that the resulting random Laguerre tessellation is well-defined, utilising the concept of tempered configurations to handle potentially unbounded weights. We then investigate how the three mixing properties - ergodicity, mixing and $α$-mixing - of the generating marked point process are preserved for the corresponding random Laguerre tessellation. Our approach combines standard approximation arguments with the properties of tempered configurations and the measurability of the Laguerre mapping.
