Functional central limit theorems for persistent Betti numbers on cylindrical networks

Johannes Krebs*, Christian Hirsch

*Corresponding author af dette arbejde

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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.

OriginalsprogEngelsk
TidsskriftScandinavian Journal of Statistics
Vol/bind49
Nummer1
Sider (fra-til)427-454
Antal sider28
ISSN0303-6898
DOI
StatusUdgivet - mar. 2022

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