论文标题
随机集的交叉点
Intersections of random sets
论文作者
论文摘要
我们考虑了经典覆盖过程的变体，即$ \ Mathbb {r}^d $中的布尔模型。以前的努力集中在无人居住的区域的融合上，该地区包含原产地为良好的限制$ c $。我们研究以局限于单位球的泊松点过程中心的集合的相交。使用交叉模型和原始布尔模型之间的耦合，我们表明缩放的交叉点弱收敛到相同的极限$ c $。在此过程中，我们提供了一些用于研究一类交叉模型的统计数据的工具。
We consider a variant of a classical coverage process, the boolean model in $\mathbb{R}^d$. Previous efforts have focused on convergence of the unoccupied region containing the origin to a well studied limit $C$. We study the intersection of sets centered at points of a Poisson point process confined to the unit ball. Using a coupling between the intersection model and the original boolean model, we show that the scaled intersection converges weakly to the same limit $C$. Along the way, we present some tools for studying statistics of a class of intersection models.
