Limit theorems for random cubical homology
Probability
2018-03-20 v2 Algebraic Topology
Abstract
This paper studies random cubical sets in . Given a cubical set , a random variable is assigned for each elementary cube in , and a random cubical set is defined by the sublevel set of consisting of elementary cubes with for each . 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.
Cite
@article{arxiv.1612.08485,
title = {Limit theorems for random cubical homology},
author = {Yasuaki Hiraoka and Kenkichi Tsunoda},
journal= {arXiv preprint arXiv:1612.08485},
year = {2018}
}
Comments
19 pages, 14 figures