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

Yasuaki Hiraoka, Tomoyuki Shirai

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

This paper studies a higher dimensional generalization of Frieze's ζ(3) -limit theorem on the d-Linial–Meshulam process. First, we define spanning acycles as a higher dimensional analogue of spanning trees, and connect its minimum weight to persistent homology. Then, our main result shows that the expected weight of the minimum spanning acycle behaves in Θ (nd−1).

Original languageEnglish
Pages (from-to)315-340
Number of pages26
JournalRandom Structures and Algorithms
Volume51
Issue number2
DOIs
Publication statusPublished - 2017 Sep

Keywords

  • Linial–Meshulam process
  • minimum spanning acycle
  • persistent homology
  • random simplicial complex

ASJC Scopus subject areas

  • Software
  • Mathematics(all)
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

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