R^(n)中凸集的汇聚概率  

The Aggregation Probability of Convex Sets in R^(n)

作　　者：严彤 邹都[1] Yan Tong;Zou Du(college of science,Wuhan University of Science and Technology,Wuhan 430081)

机构地区：[1]武汉科技大学理学院,武汉430081

出　　处：《数学物理学报(A辑)》2025年第2期619-629,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(12171378);湖北省自然科学基金(2020CFA079)。

摘　　要：利用R^(n)中凸体与平坦凸体两者平均曲率积分之间的关系,给出h个与凸体K相交的线性子空间彼此在K内相交的几何概率.在此基础上得到了在凸体K内有一个半径为r而和所有随机平面有公共点的球存在的概率,并进一步讨论了一维和二维情形下点的汇聚概率.Based on the relationship between the average curvature integrals of the convex and fat convex bodies in R^(n),the geometric probability that h linear subspaces intersecting the convex body K within K is given.On this basis,the probability of the existence of a sphere with a radius of r and a common point with all random planes in the convex body K is given.Furthermore,the convergence probabilities of the points in the one-dimensional and two-dimensional cases are discussed.

关 键 词：平均曲率积分 平行凸集 几何概率 均质积分 Minkowski和 

分 类 号：O168.5[理学—数学]