Normal approximation for subgraph count in random hypergraphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909284753735680 |
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| author | Michalczuk, Wojciech Nieradko, Mikołaj Serafin, Grzegorz |
| author_facet | Michalczuk, Wojciech Nieradko, Mikołaj Serafin, Grzegorz |
| contents | A non-uniform and inhomogeneous random hypergraph model is considered, which is a straightforward extension of the celebrated binomial random graph model $\mathbb G(n, p)$. We establish necessary and sufficient conditions for small hypergraph count to be asymptotically normal, and complement them with convergence rate in both the Wasserstein and Kolmogorov distances. Next we narrow our attention to the homogeneous model and relate the obtained results to the fourth moment phenomenon. Additionally, a short proof of necessity of aforementioned conditions is presented, which seems to be absent in the literature even in the context of the model $\mathbb G(n, p)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06112 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normal approximation for subgraph count in random hypergraphs Michalczuk, Wojciech Nieradko, Mikołaj Serafin, Grzegorz Probability Combinatorics 05C65, 05C80, 60F05 A non-uniform and inhomogeneous random hypergraph model is considered, which is a straightforward extension of the celebrated binomial random graph model $\mathbb G(n, p)$. We establish necessary and sufficient conditions for small hypergraph count to be asymptotically normal, and complement them with convergence rate in both the Wasserstein and Kolmogorov distances. Next we narrow our attention to the homogeneous model and relate the obtained results to the fourth moment phenomenon. Additionally, a short proof of necessity of aforementioned conditions is presented, which seems to be absent in the literature even in the context of the model $\mathbb G(n, p)$. |
| title | Normal approximation for subgraph count in random hypergraphs |
| topic | Probability Combinatorics 05C65, 05C80, 60F05 |
| url | https://arxiv.org/abs/2408.06112 |