Central limit theorems for the Euler characteristic in the Random Connection Model for higher-dimensional simplicial complexes
Probability
2025-06-16 v1
Abstract
As generalizations of random graphs, random simplicial complexes have been receiving growing attention in the literature. In this paper, we naturally extend the Random Connection Model (RCM), a random graph that has been extensively studied for over three decades, to a random simplicial complex, recovering many models currently found in the literature as special cases. In this new model, we derive quantitative central limit theorems for a generalized Euler characteristic in various asymptotic scenarios. We will accomplish this within a very general framework, where the vertices of the simplicial complex are drawn from an arbitrary Borel space.
Cite
@article{arxiv.2506.11918,
title = {Central limit theorems for the Euler characteristic in the Random Connection Model for higher-dimensional simplicial complexes},
author = {Dominik Pabst},
journal= {arXiv preprint arXiv:2506.11918},
year = {2025}
}