RANDOM LATTICES AND RANDOM SPHERE PACKINGS: TYPICAL PROPERTIES

被引：4
|
作者：
Shlosman, Senya [1 ,2 ]
Tsfasman, Michael A. [2 ,3 ]
机构：
[1] Ctr Phys Theor Luminy, Marseille, France
[2] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 117901, Russia
[3] Independent Univ Moscow, Moscow 121002, Russia
来源：
MOSCOW MATHEMATICAL JOURNAL | 2001年 / 1卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
Geometric density; random field; vertex covering number; sphere packing;
D O I：
10.17323/1609-4514-2001-1-1-73-89
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We review results about the density of typical lattices in R-n. This density is of the order of 2(-n). We then obtain similar results for random (non-lattice) sphere packings in R-n: after suitably taking a fraction nu of centers of spheres in a typical random packing sigma, the resulting packing tau has density C(nu)2(-n) with a reasonable C(nu). We obtain estimates of C(nu).
引用
收藏
页码：73 / 89
页数：17
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