Limit theorems for persistence diagrams

Yasuaki Hiraoka, Tomoyuki Shirai, Khanh Duy Trinh

研究成果: Article

2 引用 (Scopus)

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The persistent homology of a stationary point process on RN is studied in this paper. As a generalization of continuum percolation theory, we study higher dimensional topological features of the point process such as loops, cavities, etc. in a multiscale way. The key ingredient is the persistence diagram, which is an expression of the persistent homology. We prove the strong law of large numbers for persistence diagrams as the window size tends to infinity and give a sufficient condition for the support of the limiting persistence diagram to coincide with the geometrically realizable region. We also discuss a central limit theorem for persistent Betti numbers.

元の言語English
ページ(範囲)2740-2780
ページ数41
ジャーナルAnnals of Applied Probability
28
発行部数5
DOI
出版物ステータスPublished - 2018 10 1
外部発表Yes

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ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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