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

Abstract

Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: A limit theorem for persistence diagrams of random filtered complexes built over marked point processes, Authors: Tomoyuki Shirai, Kiyotaka Suzaki , 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.