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Functional central limit theorems for persistent Betti numbers on cylindrical networks

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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
Pages (from-to)427-454
Number of pages28
Publication statusPublished - Mar 2022

    Research areas

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

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