Random Convex Hulls and Extreme Value Statistics
Random Convex Hulls and Extreme Value Statistics
复制标题
随机凸包和极值统计
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
J. Randon
中科院分区：
文献类型：
--
作者：
S. Majumdar;A. Comtet;J. Randon
本文研究了平面上N个随机点在给定分布下的凸包的统计性质。这些点可以是独立选择的，也可以是相互关联的。在对一些零星的文献和随机凸壳问题中使用的各种方法进行了非详尽的调查之后，我们提出了一种统一的方法，基于封闭曲线的支持函数的概念和相关的柯西公式，这使我们能够准确地计算独立点和相关点情况下凸多边形包围的平均周长和平均面积。我们的方法展示了随机凸包问题和极值统计之间的美妙联系。作为相关点的一个例子，我们在这里详细研究了当这些点代表n个独立随机行走的顶点时的情况。在连续时间限制下，这减少到n个独立的平面布朗轨迹，我们精确地计算所有n个，它们的整体凸包的平均周长和平均面积。我们的结果在生态学中有相关的应用，可用于估计一群动物的活动范围。其中一些结果最近在一篇简短的通讯中公布。[j].中国农业科学，2009。
In this paper we study the statistical properties of convex hulls of N random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy’s formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of n independent random walks. In the continuum time limit this reduces to n independent planar Brownian trajectories for which we compute exactly, for all n, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. 103:140602, 2009].
影响因子：
2.5
作者：
Haushofer, Johannes;Baker, Chris I.;Kanwisher, Nancy
通讯作者：
Kanwisher, Nancy