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

TL;DR

This paper investigates the normal approximation of subgraph counts in age-dependent random networks, establishing asymptotic normality for cliques and subtrees using advanced probabilistic methods.

Contribution

It provides new results on the asymptotic normality of subgraph counts in age-dependent models, employing Malliavin-Stein and CLT techniques.

Findings

Normal approximation for clique counts established.

Distributional convergence for subtree counts proved.

Results applicable in the light-tailed regime with finite moments.

Abstract

We study normal approximation of subgraph counts in a model of spatial scale-free random networks known as the age-dependent random connection model. In the light-tailed regime where only moments of order $(2 + \varepsilon)$ are finite, we study the asymptotic normality of both clique and subtree counts. For clique counts, we establish a multivariate quantitative normal approximation result through the Malliavin-Stein method. In the more delicate case of subtree counts, we obtain distributional convergence based on a central limit theorem for sequences of associated random variables.