Cluster-size decay in supercritical kernel-based spatial random graphs

Joost Jorritsma, Júlia Komjáthy, Dieter Mitsche

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We consider a large class of spatially-embedded random graphs that includes among others long-range percolation, continuum scale-free percolation and the age-dependent random connection model. We assume that the parameters are such that there is an infinite component. We identify the stretch-exponent $\zeta\in(0,1)$ of the subexponential decay of the cluster-size distribution. That is, with $|\mathcal{C}(0)|$ denoting the number of vertices in the component of the vertex at $0\in \mathbb{R}^d$, we prove \[ \mathbb{P}(k\le |\mathcal{C}(0)|
Original languageEnglish
Publication statusPublished - 1 Mar 2023

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