Limit theorems under heavy-tailed scenario in the age dependent random connection models
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929491901677568 |
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| author | Hirsch, Christian Owada, Takashi |
| author_facet | Hirsch, Christian Owada, Takashi |
| contents | This paper considers limit theorems associated with subgraph counts in the age-dependent random connection model. First, we identify regimes where the count of sub-trees converges weakly to a stable random variable under suitable assumptions on the shape of trees. The proof relies on an intermediate result on weak convergence of associated point processes towards a Poisson point process. Additionally, we prove the same type of results for the clique counts. Here, a crucial ingredient includes the expectation asymptotics for clique counts, which itself is a result of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit theorems under heavy-tailed scenario in the age dependent random connection models Hirsch, Christian Owada, Takashi Probability 60D05, 60G70 This paper considers limit theorems associated with subgraph counts in the age-dependent random connection model. First, we identify regimes where the count of sub-trees converges weakly to a stable random variable under suitable assumptions on the shape of trees. The proof relies on an intermediate result on weak convergence of associated point processes towards a Poisson point process. Additionally, we prove the same type of results for the clique counts. Here, a crucial ingredient includes the expectation asymptotics for clique counts, which itself is a result of independent interest. |
| title | Limit theorems under heavy-tailed scenario in the age dependent random connection models |
| topic | Probability 60D05, 60G70 |
| url | https://arxiv.org/abs/2409.05226 |