论文标题
在单位球中随机凸出的凸壳剥离的第一层的限制理论
Limit theory for the first layers of the random convex hull peeling in the unit ball
论文作者
论文摘要
点集的凸壳剥离是通过取下集合的凸壳并在内部点上重复迭代的操作，直到没有点仍然保留为止。每个船体的边界称为一层。我们研究了均匀的载体载体的第一层的k维面和外部缺陷的固有体积，该凸载体剥离的单位球的强度为无限。更确切地说，我们为他们的期望和差异以及中心限制定理提供了渐近限制。特别是，增长率不取决于该层。
The convex hull peeling of a point set is obtained by taking the convex hull of the set and repeating iteratively the operation on the interior points until no point remains. The boundary of each hull is called a layer. We study the number of k-dimensional faces and the outer defect intrinsic volumes of the first layers of the convex hull peeling of a homogeneous Poisson point process in the unit ball whose intensity goes to infinity. More precisely we provide asymptotic limits for their expectation and variance as well as a central limit theorem. In particular, the growth rates do not depend on the layer.
