Normal approximation of subgraph counts in the random-connection model
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917067778686976 |
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| author | Liu, Qingwei Privault, Nicolas |
| author_facet | Liu, Qingwei Privault, Nicolas |
| contents | This paper derives normal approximation results for subgraph counts written as multiparameter stochastic integrals in a random-connection model based on a Poisson point process. By combinatorial arguments we express the cumulants of general subgraph counts using sums over connected partition diagrams, after cancellation of terms obtained by Möbius inversion. Using the Statulevičius condition, we deduce convergence rates in the Kolmogorov distance by studying the growth of subgraph count cumulants as the intensity of the underlying Poisson point process tends to infinity. Our analysis covers general subgraphs in the dilute and full random graph regimes, and tree-like subgraphs in the sparse random graph regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_12145 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Normal approximation of subgraph counts in the random-connection model Liu, Qingwei Privault, Nicolas Probability 60F05, 60D05, 05C80, 60G55 This paper derives normal approximation results for subgraph counts written as multiparameter stochastic integrals in a random-connection model based on a Poisson point process. By combinatorial arguments we express the cumulants of general subgraph counts using sums over connected partition diagrams, after cancellation of terms obtained by Möbius inversion. Using the Statulevičius condition, we deduce convergence rates in the Kolmogorov distance by studying the growth of subgraph count cumulants as the intensity of the underlying Poisson point process tends to infinity. Our analysis covers general subgraphs in the dilute and full random graph regimes, and tree-like subgraphs in the sparse random graph regime. |
| title | Normal approximation of subgraph counts in the random-connection model |
| topic | Probability 60F05, 60D05, 05C80, 60G55 |
| url | https://arxiv.org/abs/2301.12145 |