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 tessellations such as 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.

中文翻译：

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平面镶嵌的指数矩

在本文中，我们展示了基于驻点过程的平面镶嵌系列的单位圆盘中总边长的所有指数矩的存在。除了经典的镶嵌，如 Poisson-Voronoi、Poisson-Delaunay 和 Poisson 线镶嵌，我们还处理 Johnson-Mehl 镶嵌、曼哈顿网格、嵌套版本和 Palm 版本。作为我们证明的一部分，对于一些平面镶嵌，我们还推导出与单元盘相交的单元数和边数的指数矩的存在。