Random points in halfspheres
Random points in halfspheres
复制标题
半球体中的随机点
DOI：
10.1002/rsa.20644
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发表时间：
2015
影响因子：
1
通讯作者：
R. Schneider
中科院分区：
文献类型：
--
作者：
I. Bárány;D. Hug;M. Reitzner;R. Schneider
本文所考虑的球凸集K <$Sd中的随机球多面体Pn是K中n个独立的均匀分布的随机点的球船体。对于包含在开半球中的球凸集K，Pn的行为与欧氏空间中类似生成的随机凸多面体的行为非常相似，但K是半球时的情况不同。这就是我们在这里调查，建立的渐近行为，n趋于无穷大，期望的几个特性的Pn，如刻面和顶点数，体积和表面积。对于Hausdorff距离，我们也得到了一些几乎必然的渐近估计。© 2016 Wiley Periodicals，Inc.随机结构算法，2017年3月50日至22日
A random spherical polytope Pn in a spherically convex set K⊂Sd as considered here is the spherical convex hull of n independent, uniformly distributed random points in K. The behaviour of Pn for a spherically convex set K contained in an open halfsphere is quite similar to that of a similarly generated random convex polytope in a Euclidean space, but the case when K is a halfsphere is different. This is what we investigate here, establishing the asymptotic behaviour, as n tends to infinity, of the expectation of several characteristics of Pn, such as facet and vertex number, volume and surface area. For the Hausdorff distance from the halfsphere, we obtain also some almost sure asymptotic estimates. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 3–22, 2017