Various mixing properties of $\beta$-, ${\beta }^{\prime }$- and Gaussian-Delaunay tessellations in ${ℝ}^{d-1}$ are studied. It is shown that these tessellation models are absolutely regular, or $\beta$-mixing. In the $\beta$- and the Gaussian case exponential bounds for the absolute regularity coefficients are found. In the ${\beta }^{\prime }$-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 $\beta$- and Gaussian-Delaunay tessellations are established. This includes the number of $k$-dimensional faces and the $k$-volume of the $k$-skeleton for $k\in \{0,1,\dots ,d-1\}$.

各种混合特性$\beta$-,${\beta }^{\prime }$- 以及 Gaussian-Delaunay 镶嵌${ℝ}^{d-1}$被研究。结果表明，这些镶嵌模型是绝对规则的，或者$\beta$-混合。在里面$\beta$- 并找到绝对正则系数的高斯情况指数界限。在里面${\beta }^{\prime }$-情况下，这些系数仅显示多项式衰减。在此背景下，基础建设的稳定半径出现了新的、强烈的集中界限。使用绝对规则平稳随机镶嵌的通用装置，许多几何参数的中心极限定理$\beta$- 并建立高斯-德洛内曲面细分。这包括数量$k$维度面和$k$-体积$k$-骨架$k\epsilon \{0,1,\dots \dots ,d-1\}$。