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arXiv · 2103.08868

A limit theorem for persistence diagrams of random filtered complexes built over marked point processes

Tomoyuki Shirai·Kiyotaka Suzaki
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Abstract

We consider random filtered complexes built over marked point processes on Euclidean spaces. Examples of our filtered complexes include a filtration of $\check{\textrm{C}}$ech complexes of a family of sets with various sizes, growths, and shapes. We establish the law of large numbers for persistence diagrams as the size of the convex window observing a marked point process tends to infinity.

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Tomoyuki Shirai, Kiyotaka Suzaki. 2021-03-16. A limit theorem for persistence diagrams of random filtered complexes built over marked point processes. https://arxiv.org/abs/2103.08868

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