Limit theorems for critical faces above the vanishing threshold
Autor: | Wei, Zifu, Owada, Takashi, Yogeshwaran, D. |
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Rok vydání: | 2023 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | We investigate convergence of point processes associated with critical faces for a \v{C}ech filtration built over a homogeneous Poisson point process in the $d$-dimensional flat torus. The convergence of our point process is established in terms of the $\mathcal M_0$-topology, when the connecting radius of a \v{C}ech complex decays to $0$, so slowly that critical faces are even less likely to occur than those in the regime of threshold for homological connectivity. We also obtain a series of limit theorems for positive and negative critical faces, all of which are considerably analogous to those for critical faces. Comment: 21 pages; Minor notational and typographical edits made |
Databáze: | arXiv |
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