Strong Law of Large Numbers for Betti Numbers in the Thermodynamic Regime

Akshay Goel*, Khanh Duy Trinh, Kenkichi Tsunoda

*この研究の対応する著者

研究成果: Article査読

4 被引用数 (Scopus)

抄録

We establish the strong law of large numbers for Betti numbers of random Čech complexes built on R N -valued binomial point processes and related Poisson point processes in the thermodynamic regime. Here we consider both the case where the underlying distribution of the point processes is absolutely continuous with respect to the Lebesgue measure on R N and the case where it is supported on a C 1 compact manifold of dimension strictly less than N. The strong law is proved under very mild assumption which only requires that the common probability density function belongs to L p spaces, for all 1 ≤ p< ∞.

本文言語English
ページ(範囲)865-892
ページ数28
ジャーナルJournal of Statistical Physics
174
4
DOI
出版ステータスPublished - 2019 2 28
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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