Abstract:As generalizations of random graphs, random simplicial complexes have attracted growing attention in the literature. In this paper, we introduce a new random simplicial complex that extends the Random Connection Model (RCM), a random graph model that has been extensively studied for over three decades, to higher-dimensional simplicial complexes. The resulting model allows simplices of different dimensions to be governed by separate connection functions, providing a higher-dimensional analogue of the RCM. For this model, we derive explicit moment formulas for a generalized Euler characteristic and establish quantitative central limit theorems under increasing intensity and increasing observation windows. To this end, we extend existing normal approximation results for Poisson functionals to a class of generalized difference operators. These results are obtained in a general framework in which the vertices of the simplicial complex are drawn from an arbitrary Borel space. In the stationary Euclidean setting with marks, we additionally establish a multivariate central limit theorem for simplex counts.
From: Dominik Pabst [view email]
[v1]
Fri, 13 Jun 2025 16:10:25 UTC (1,758 KB)
[v2]
Fri, 28 Aug 2026 21:54:00 UTC (1,760 KB)
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