n边平面Voronoi原胞的渐近统计:II。试探法
Asymptotic statistics of the n-sided planar Voronoi cell: II. Heuristics
摘要:
我们开发了一套启发式的参数来解释几个结果平面Poisson-Voronoi镶嵌,得出了相当大的数学努力的成本。结果涉及的Voronoi细胞具有大量的n边。这些论点从应用于围绕中心细胞的n个邻居的排列的熵平衡开始。然后对任意胞元为n边的概率p_n的相空间积分进行了简化计算。指出了论证的局限性。作为一个新的应用程序,我们计算的预期数量的加布里埃尔(或充分)邻居的n边细胞在大n极限。
英文摘要:
We develop a set of heuristic arguments to explain several results on planar Poisson-Voronoi tessellations that were derived earlier at the cost of considerable mathematical effort. The results concern Voronoi cells having a large number n of sides. The arguments start from an entropy balance applied to the arrangement of n neighbors around a central cell. It is followed by a simplified evaluation of the phase space integral for the probability p_n that an arbitrary cell be n-sided. The limitations of the arguments are indicated. As a new application we calculate the expected number of Gabriel (or full) neighbors of an n-sided cell in the large-n limit.
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