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.
引用
收藏
页码：665 / 687
页数：23
相关论文
共 50 条
  • [1] Limit Theorems for Random Cubical Homology
    Yasuaki Hiraoka
    Kenkichi Tsunoda
    Discrete & Computational Geometry, 2018, 60 : 665 - 687
  • [2] Limit theorems for random walks
    Bendikov, Alexander
    Cygan, Wojciech
    Trojan, Bartosz
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2017, 127 (10) : 3268 - 3290
  • [3] Limit Theorems for “Random Flights”
    Davydov Y.A.
    Journal of Mathematical Sciences, 2023, 273 (5) : 755 - 762
  • [4] Limit theorems for random Dirichlet series
    Buraczewski, Dariusz
    Dong, Congzao
    Iksanov, Alexander
    Marynych, Alexander
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2023, 165 : 246 - 274
  • [5] Limit theorems for random degenerate diffusions
    Department of Mathematics, Hong Kong Univ. of Sci. and Technol., Clear Water Bay, Kowloon, Hong Kong
    不详
    Nonlinear Anal Theory Methods Appl, 1 PART 1 (211-222):
  • [6] RANDOM SET LIMIT-THEOREMS
    CRESSIE, N
    ADVANCES IN APPLIED PROBABILITY, 1979, 11 (02) : 281 - 282
  • [7] ON LIMIT THEOREMS FOR PRODUCT OF RANDOM MATRICES
    TUTUBALIN, VN
    THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1965, 10 (01): : 15 - +
  • [8] Central limit theorems for random polytopes
    Matthias Reitzner
    Probability Theory and Related Fields, 2005, 133 : 483 - 507
  • [9] SOME LIMIT THEOREMS FOR A RANDOM DETERMINANT
    GVIKO, VL
    DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR, 1972, (04): : 300 - &
  • [10] RANDOM CENTRAL LIMIT THEOREMS FOR MARTINGALES
    RAO, BLS
    ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1969, 20 (1-2): : 217 - &
12345