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Limit theorems under heavy-tailed scenario in the age dependent random connection models
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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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Normal approximation for subgraph counts in age-dependent random connection models
Clique and subtree counts in the age-dependent random connection model are asymptotically normal in the light-tailed regime, with quantitative bounds for cliques.
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