Functional central limit theorems for persistent Betti numbers on cylindrical networks

6Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

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 Čech 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

CITATION STYLE

APA

Krebs, J., & Hirsch, C. (2022). Functional central limit theorems for persistent Betti numbers on cylindrical networks. Scandinavian Journal of Statistics, 49(1), 427–454. https://doi.org/10.1111/sjos.12524

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free