Limit Theorems for Random Cubical Homology

被引：4
|
作者：
Hiraoka, Yasuaki [1 ,2 ]
Tsunoda, Kenkichi [2 ,3 ]
机构：
[1] Kyoto Univ, Inst Adv Study, Sakyo Ku, Yoshida Ushinomiya Cho, Kyoto 6068501, Japan
[2] RIKEN, Ctr Adv Intelligence Project, Tokyo 1030027, Japan
[3] Osaka Univ, Grad Sch Sci, Dept Math, 1-1 Machikaneyama Cho, Toyonaka, Osaka 5600043, Japan
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2018年 / 60卷 / 03期
关键词：
Random topology; Cubical complex; Cubical homology; Betti number; RANDOM SIMPLICIAL COMPLEXES;
D O I：
10.1007/s00454-018-0007-z
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
This paper studies random cubical sets in R-d. Given a cubical set X. R-d, a random variable.Q. [0, 1] is assigned for each elementary cube Q in X, and a random cubical set X(t) is defined by the sublevel set of X consisting of elementary cubes with.Q <= t for each t. [0, 1]. Under this setting, the main results of this paper show the limit theorems (law of large numbers and central limit theorem) for Betti numbers and lifetime sums of random cubical sets and filtrations. In addition to the limit theorems, the positivity of the limiting Betti numbers is also shown.
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页码：665 / 687
页数：23
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