## 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 |
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ページ（範囲） | 865-892 |

ページ数 | 28 |

ジャーナル | Journal of Statistical Physics |

巻 | 174 |

号 | 4 |

DOI | |

出版ステータス | Published - 2019 2月 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