Minimum spanning acycle and lifetime of persistent homology in the Linial–Meshulam process1. Issue 2 (18th April 2017)

• Record Type: Journal Article
• Authors: Hiraoka, Yasuaki; Shirai, Tomoyuki
• Is Part Of: Random structures & algorithms. Volume 51:Issue 2(2017)
• Page Start: 315
• Page End: 340
• Publication Date: 2017-04-18
• Subjects: random simplicial complex -- minimum spanning acycle -- Linial–Meshulam process -- persistent homology; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20718
• Languages: English
• ISSNs: 1042-9832

Abstract

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 ) . © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 315–340, 2017