Geometrical Probability and Random Points on a Hypersphere
نویسندگان
چکیده
منابع مشابه
Geometrical Probability and Random Points on a Hypersphere
0. Summary. This paper is concerned with the properties of convex cones and their dual cones generated by points randomly distributed on the surface of a d-sphere. For radially symmetric distributions on the points, the expected nGmber of k-faces and natural measure of the set of k-faces will be found. The expected number of vertices, or extreme points, of convex hulls of random points in E~ an...
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Thus for fc ̂ 4 8k = fc/2 1. The value of fc which has received the greatest attention is fc = 2, the number of lattice points in a circle. Wilton [2] gives an account of the early work in this problem. Since that time several results have been published establishing new values of 8 for which P2(x) = 0(xe). One of the most recent is Chen Jing-ren's proof [3] that P2(x) = 0(x12/37). Hardy (see [2...
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1967
ISSN: 0003-4851
DOI: 10.1214/aoms/1177699073