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

2024/09/08 by Christian Hirsch, Hirsch, Christian, Takashi Owada +1 · 1 citation
Decision Sciences · Mathematics · #60D05 #60G70 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Simulation Techniques and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2409.05226

openalex publication_date 2024/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Normal approximation for subgraph counts in age-dependent random connection models

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