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

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 left parenthesis 2 plus epsilon right parenthesis ( 2 + ε ) $(2+\varepsilon)$ 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.