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

Christian Hirsch and Takashi Owada

Stochastic Processes and their Applications, 2026, vol. 192, issue C

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.

Keywords: Stable limit theorem; Extreme value theory; Sub-tree count; Clique count; Scale-free network; Random connection model (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104815

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