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Normal approximation for statistics of randomly weighted complexes
Shu Kanazawa, Khanh Duy Trinh, D. Yogeshwaran
We prove normal approximation bounds for statistics of randomly weighted (simplicial) complexes. In particular, we consider the complete -dimensional complex on vertices wit…
Large deviation principle for persistence diagrams of random cubical filtrations
Yasuaki Hiraoka, Shu Kanazawa, Jun Miyanaga +1
The objective of this article is to investigate the asymptotic behavior of the persistence diagrams of a random cubical filtration as the window size tends to infinity. Here, a ran…
Law of large numbers for Betti numbers of homogeneous and spatially independent random simplicial complexes
Shu Kanazawa
The Linial-Meshulam complex model is a natural higher-dimensional analog of the Erdős-Rényi graph model. In recent years, Linial and Peled established a limit theorem for Betti num…
Asymptotic behavior of lifetime sums for random simplicial complex processes
Masanori Hino, Shu Kanazawa
We study the homological properties of random simplicial complexes. In particular, we obtain the asymptotic behavior of lifetime sums for a class of increasing random simplicial co…