$β$-Delaunay曲面细分IV：混合性质和中心极限定理
The $β$-Delaunay tessellation IV: Mixing properties and central limit theorems
摘要：
研究了$\mathbb{R}^{d-1}$中$β$-、$β'$-和Gaussian Delaunay镶嵌的各种混合性质。结果表明，这些细分模型是绝对规则的，或$β$-混合。在$β$-和Gaussian情形下，绝对正则性系数都有指数界，而在$β'$-情形下，这些系数只表现为多项式衰减。在背景是新的和强大的浓度范围内的半径稳定的基础建设。利用绝对正则平稳随机镶嵌的一般方法，建立了$β$-和Gaussian Delaunay镶嵌的若干几何参数的中心极限定理.这包括$k$维面的数量和$k$-sk的$k$-体积
英文摘要：
Various mixing properties of $β$-, $β'$- and Gaussian Delaunay tessellations in $\mathbb{R}^{d-1}$ are studied. It is shown that these tessellation models are absolutely regular, or $β$-mixing. In the $β$- and the Gaussian case exponential bounds for the absolute regularity coefficients are found. In the $β'$-case these coefficients show a polynomial decay only. In the background are new and strong concentration bounds on the radius of stabilization of the underlying construction. Using a general device for absolutely regular stationary random tessellations, central limit theorems for a number of geometric parameters of $β$- and Gaussian Delaunay tessellations are established. This includes the number of $k$-dimensional faces and the $k$-volume of the $k$-sk
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