Limit theorems under heavy-tailed scenario in the age dependent random connection models

Christian Hirsch; Takashi Owada

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arXiv · 2409.05226

Limit theorems under heavy-tailed scenario in the age dependent random connection models

Christian Hirsch·Takashi Owada

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Abstract

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.

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Christian Hirsch, Takashi Owada. 2024-09-08. Limit theorems under heavy-tailed scenario in the age dependent random connection models. https://arxiv.org/abs/2409.05226

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