论文标题
$β$ -Delaunay tessellation i：典型单元的模型和几何形状的描述
The $β$-Delaunay tessellation I: Description of the model and geometry of typical cells
论文作者
论文摘要
在本文中，引入了两种新类别的固定随机简单性镶嵌，即所谓的$β$ - 和$β'$ - $ - delaunay tessellations。他们的构建基于时空抛物面壳过程，并概括了经典的泊松 - 二奈尼镶嵌液的过程。明确鉴定了体积功率加权典型细胞的分布，从而建立了与$β$ - 和$β'$ - 多面体类别的显着联系。这些表示形式用于确定此类细胞的主要特征，包括体积矩，预期角度和细胞强度。
In this paper two new classes of stationary random simplicial tessellations, the so-called $β$- and $β'$-Delaunay tessellations, are introduced. Their construction is based on a space-time paraboloid hull process and generalizes that of the classical Poisson-Delaunay tessellation. The distribution of volume-power weighted typical cells is explicitly identified, establishing thereby a remarkable connection to the classes of $β$- and $β'$-polytopes. These representations are used to determine principal characteristics of such cells, including volume moments, expected angle sums and cell intensities.
