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

Yasuaki Hiraoka; Tomoyuki Shirai

doi:10.1002/rsa.20718

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

Yasuaki Hiraoka, Tomoyuki Shirai

Division of Fundamental mathematics

Research output: Contribution to journal › Article › peer-review

13 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 (n^d−1).

Original language	English
Pages (from-to)	315-340
Number of pages	26
Journal	Random Structures and Algorithms
Volume	51
Issue number	2
DOIs	https://doi.org/10.1002/rsa.20718
Publication status	Published - Sep 2017

All Science Journal Classification (ASJC) codes

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

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10.1002/rsa.20718

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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).",

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

Abstract

All Science Journal Classification (ASJC) codes

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