平面镶嵌的指数矩
Exponential moments for planar tessellations
摘要：
在本文中，我们证明了存在的所有指数矩的总边长在一个单位圆盘的平面镶嵌族的基础上的驻点过程。除了经典的这样的镶嵌，如Poisson-Voronoi，Poisson-Delaunay和泊松线镶嵌，我们也对待约翰逊-梅尔镶嵌，曼哈顿网格，嵌套版本和Palm版本。作为我们的证明的一部分，对于一些平面镶嵌，我们还得到了存在的指数矩的细胞的数量和相交的单位圆盘的边缘的数量。
英文摘要：
In this paper we show existence of all exponential moments for the total edge length in a unit disk for a family of planar tessellations based on stationary point processes. Apart from classical such tessellations like the Poisson-Voronoi, Poisson-Delaunay and Poisson line tessellation, we also treat the Johnson-Mehl tessellation, Manhattan grids, nested versions and Palm versions. As part of our proofs, for some planar tessellations, we also derive existence of exponential moments for the number of cells and the number of edges intersecting the unit disk.
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