November 2024 Normal approximation of subgraph counts in the random-connection model
Qingwei Liu, Nicolas Privault
Author Affiliations +
Bernoulli 30(4): 3224-3250 (November 2024). DOI: 10.3150/23-BEJ1712

Abstract

This paper derives normal approximation results for subgraph counts written as multiparameter stochastic integrals in a random-connection model based on a Poisson point process. By combinatorial arguments we express the cumulants of general subgraph counts using sums over connected partition diagrams, after cancellation of terms obtained by Möbius inversion. Using the Statulevičius condition, we deduce convergence rates in the Kolmogorov distance by studying the growth of subgraph count cumulants as the intensity of the underlying Poisson point process tends to infinity. Our analysis covers general subgraphs in the dilute and full random graph regimes, and tree-like subgraphs in the sparse random graph regime.

Acknowledgments

We thank M. Schulte and C. Thäle for a correction to an earlier version of Lemma 2.8, and the anonymous referees for useful suggestions. This research is supported by the Ministry of Education, Singapore, under its Tier 2 Grant MOE-T2EP20120-0005.

Citation

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Qingwei Liu. Nicolas Privault. "Normal approximation of subgraph counts in the random-connection model." Bernoulli 30 (4) 3224 - 3250, November 2024. https://doi.org/10.3150/23-BEJ1712

Information

Received: 1 June 2023; Published: November 2024
First available in Project Euclid: 30 July 2024

Digital Object Identifier: 10.3150/23-BEJ1712

Keywords: cumulant method , Kolmogorov distance , Normal approximation , Poisson point process , Random graphs , random-connection model , subgraph count

Vol.30 • No. 4 • November 2024
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