Functional central limit theorems for persistent Betti numbers on cylindrical networks

Johannes Krebs and Christian Hirsch

Scandinavian Journal of Statistics, 2022, vol. 49, issue 1, 427-454

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.

Date: 2022
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