Minimum spanning acycle and lifetime of persistent homology in the Linial–Meshulam process |
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| Authors: | Yasuaki Hiraoka Tomoyuki Shirai |
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| Affiliation: | 1. WPI ‐ Advanced Institute for Materials Research (WPI‐AIMR), Tohoku University, Aoba‐ku, Sendai, Japan;2. Institute of Mathematics for Industry, Kyushu University, Nishi‐ku, Fukuoka, Japan |
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| Abstract: | This paper studies a higher dimensional generalization of Frieze's  ‐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  . © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 315–340, 2017 |
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| Keywords: | random simplicial complex minimum spanning acycle Linial– Meshulam process persistent homology |
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‐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 
. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 315–340, 2017