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arXiv · 2003.13490

Functional central limit theorems for persistent Betti numbers on cylindrical networks

Johannes Krebs·Christian Hirsch
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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.

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Johannes Krebs, Christian Hirsch. 2020-03-30. Functional central limit theorems for persistent Betti numbers on cylindrical networks. https://arxiv.org/abs/2003.13490

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