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

Published: 13 September 2022
by  VTeX

Abstract: Random filtered complexes built over marked point processes on Euclidean spaces are considered. Examples of these filtered complexes include a filtration of $\check{\text{C}}$ech complexes of a family of sets with various sizes, growths, and shapes. The law of large numbers for persistence diagrams is established as the size of the convex window observing a marked point process tends to infinity.
Keywords: Marked point process / persistence diagram / persistent Betti number / random topology

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