论文标题
泊松驱动点过程的泊松近似和随机几何形状中的极端值
Poisson approximation of Poisson-driven point processes and extreme values in stochastic geometry
论文作者
论文摘要
我们研究了由基础泊松过程的某些点元中心组成的点过程。在描述泊松过程的几何特性的各种功能的超出函数的研究中，随机几何形状出现了这种过程。我们使用该点过程与其棕榈版的耦合来证明一般的泊松限制定理。然后，我们将一般结果与随机镶嵌物中大细胞（肯德尔问题）的渐近形状理论相结合，并证明泊松定理的大细胞定理（相对于一般大小的功能）在泊松 - 沃罗诺伊和delaunay mosaic中。结果，我们为混凝土尺寸功能的渐近分布建立了牙龈限制，并指定收敛速率。这扩展了Calka和Chenavier（2014）和Chenavier（2014）的极端价值。
We study point processes that consist of certain centers of point tuples of an underlying Poisson process. Such processes arise in stochastic geometry in the study of exceedances of various functionals describing geometric properties of the Poisson process. We use a coupling of the point process with its Palm version to prove a general Poisson limit theorem. We then combine our general result with the theory of asymptotic shapes of large cells (Kendall's problem) in random mosaics and prove Poisson limit theorems for large cells (with respect to a general size functional) in the Poisson-Voronoi and -Delaunay mosaic. As a consequence, we establish Gumbel limits for the asymptotic distribution of concrete size functionals and specify the rate of convergence. This extends extreme value results from Calka and Chenavier (2014) and Chenavier (2014).
