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

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  • Hirsch, Christian
  • Owada, Takashi

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.

Suggested Citation

  • Hirsch, Christian & Owada, Takashi, 2026. "Limit theorems under heavy-tailed scenario in the age-dependent random connection models," Stochastic Processes and their Applications, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:spapps:v:192:y:2026:i:c:s0304414925002595
    DOI: 10.1016/j.spa.2025.104815
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    References listed on IDEAS

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    1. Peter Gracar & Arne Grauer & Lukas Lüchtrath & Peter Mörters, 2019. "The age-dependent random connection model," Queueing Systems: Theory and Applications, Springer, vol. 93(3), pages 309-331, December.
    2. Komjáthy, Júlia & Lodewijks, Bas, 2020. "Explosion in weighted hyperbolic random graphs and geometric inhomogeneous random graphs," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1309-1367.
    3. Christian Hirsch & Peter Juhasz, 2025. "On the Topology of Higher-order Age-dependent Random Connection Models," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-41, June.
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