Functional central limit theorems for persistent Betti numbers on cylindrical networks

Johannes Krebs*, Christian Hirsch

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

18 Downloads (Pure)

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.

Original languageEnglish
JournalScandinavian Journal of Statistics
Volume49
Issue1
Pages (from-to)427-454
Number of pages28
ISSN0303-6898
DOIs
Publication statusPublished - Mar 2022

Keywords

  • functional central limit theorems
  • goodness&#8208
  • of&#8208
  • fit tests
  • graphical networks
  • persistent Betti numbers
  • stochastic geometry
  • topological data analysis

Fingerprint

Dive into the research topics of 'Functional central limit theorems for persistent Betti numbers on cylindrical networks'. Together they form a unique fingerprint.

Cite this