Functional central limit theorems for persistent Betti numbers on cylindrical networks
Statistics Theory
2021-02-26 v2 Methodology
Statistics Theory
Abstract
We study functional central limit theorems for persistent Betti numbers obtained from networks defined on a Poisson point process. The limit is formed in large volumes of cylindrical shape stretching only in one dimension. The results cover a directed sublevel-filtration for stabilizing networks and the Cech and Vietoris-Rips complex on the random geometric graph. The presented functional central limit theorems open the door to a variety of statistical applications in topological data analysis and we consider goodness-of-fit tests in a simulation study.
Cite
@article{arxiv.2003.13490,
title = {Functional central limit theorems for persistent Betti numbers on cylindrical networks},
author = {Johannes Krebs and Christian Hirsch},
journal= {arXiv preprint arXiv:2003.13490},
year = {2021}
}