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Functional central limit theorems for persistent Betti numbers on cylindrical networks
Author(s) -
Krebs Johannes,
Hirsch Christian
Publication year - 2022
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12524
Subject(s) - betti number , mathematics , limit (mathematics) , central limit theorem , cover (algebra) , point process , poisson point process , poisson distribution , dimension (graph theory) , filtration (mathematics) , combinatorics , graph , pure mathematics , discrete mathematics , topology (electrical circuits) , mathematical analysis , statistics , mechanical engineering , engineering
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.