Percolation in the marked stationary Random Connection Model for higher-dimensional simplicial complexes
Abstract
We introduce a novel percolation model that generalizes the classical Random Connection Model (RCM) to a random simplicial complex, allowing for a more refined understanding of connectivity and emergence of large-scale structures in random topological spaces. Regarding percolation with respect to the notion of up-connectivity, we establish the existence of a sharp phase transition for the appearance of a giant component, akin to the well-known threshold behavior in random graphs. This sharp phase transition is, in its generality, new even for the classical RCM as a random graph. As special cases, we obtain sharp phase transitions for the Vietoris-Rips complex, the Cech complex, and the Boolean model, allowing us to identify which properties of these well-known percolation models are actually required.
Cite
@article{arxiv.2506.15038,
title = {Percolation in the marked stationary Random Connection Model for higher-dimensional simplicial complexes},
author = {Dominik Pabst},
journal= {arXiv preprint arXiv:2506.15038},
year = {2025}
}