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[We discuss a higher-dimensional analogue of Frieze’s ζ(3)-limit theorem for the Erdős–Rényi graph process applied to a family of increasing random simplicial complexes. In particular, we consider the time integrals of Betti numbers, which are interpreted as lifetime sums in the context of persistent homologies. We survey some recent results regarding their asymptotic behavior that answer some questions posed in an earlier study by Hiraoka and Shirai.]
Published: Mar 24, 2021
Keywords: Random simplicial complex; Betti number; Persistent homology; Lifetime sum; Primary: 60D05; Secondary: 05C80; 55U10; 05E45; 60C05
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