三维Poisson-Voronoi曲面细分中n边面的精确渐近统计
Exact asymptotic statistics of the n-edged face in a 3D Poisson-Voronoi tessellation
摘要：
我们考虑3D Poisson-Voronoi曲面细分。本文研究了任意选取的n边细胞面和相邻细胞种子之间的距离等于2L时的联合概率分布pi_n（L）。我们导出这个量的精确表达式，在极限n-> infty中有效，其中n ^{1/6} L固定。确定了首阶修正项。较早的Monte Carlo数据得到了很好的协议。细胞表面被一个三维的排除域所包围，该排除域是n个球的联合;它是南瓜形的，类似于2D Voronoi细胞的花。对于n-> infty，该域趋向于相等大小半径的环面。半径的比例为n ^{1/3}，与早期的启发式工作一致。我们实现了其他几个统计特性的n边细胞面的详细了解。
英文摘要：
We consider the 3D Poisson-Voronoi tessellation. We investigate the joint probability distribution pi_n(L) for an arbitrarily selected cell face to be n-edged and for the distance between the seeds of its adjacent cells to be equal to 2L. We derive an exact expression for this quantity, valid in the limit n->infty with n^{1/6}L fixed. The leading order correction term is determined. Good agreement with earlier Monte Carlo data is obtained. The cell face is surrounded by a three-dimensional excluded domain that is the union of n balls; it is pumpkin-shaped and analogous to the flower of the 2D Voronoi cell. For n->infty this domain tends towards a torus of equal major and minor radii. The radii scale as n^{1/3}, in agreement with earlier heuristic work. We achieve a detailed understanding of several other statistical properties of the n-edged cell face.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
