Minimum spanning acycle and lifetime of persistent homology in the Linial-Meshulam process

DOI10.1002/rsa.20718zbMath1370.05190arXiv1503.05669OpenAlexW2963542001MaRDI QIDQ5357982

Yasuaki Hiraoka, Tomoyuki Shirai

Publication date: 18 September 2017

Published in: Random Structures & Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.05669

zbMATH Keywords

persistent homologyrandom simplicial complexLinial-Meshulam processminimum spanning acycle

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Combinatorial aspects of simplicial complexes (05E45)

Related Items (13)

Limit theorems for persistence diagrams ⋮ Limit theorems for Betti numbers of extreme sample clouds with application to persistence barcodes ⋮ A higher-dimensional homologically persistent skeleton ⋮ Random Simplicial Complexes: Models and Phenomena ⋮ Homological connectivity in random Čech complexes ⋮ Field choice problem in persistent homology ⋮ Thresholds for vanishing of `isolated' faces in random Čech and Vietoris-Rips complexes ⋮ Limit theorems for random cubical homology ⋮ Asymptotics of integrals of Betti numbers for random simplicial complex processes ⋮ Limit theorems for topological invariants of the dynamic multi-parameter simplicial complex ⋮ On the choice of weight functions for linear representations of persistence diagrams ⋮ Asymptotic behavior of lifetime sums for random simplicial complex processes ⋮ Minimum weight disk triangulations and fillings

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