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.
年龄相关随机连接模型重尾情况下的极限定理
本文研究了与年龄相关随机连接模型中子图计数相关的极限定理。首先,我们确定了在适当的树形假设下,子树数量弱收敛于稳定随机变量的情形。这一证明依赖于相关点过程向泊松点过程弱收敛的中间结果。此外,我们还证明了小块计数的同类结果。在这里,一个关键要素包括小块计数的期望渐近,这本身就是一个独立的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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