Likelihood of Borromean component formation in randomly linked ring networks

Determine the probability with which Borromean components form in networks of randomly linked rings, quantifying how often such three-body links arise in disordered ring systems.

Background

Previous lattice-based studies established percolation behavior in idealized Borromean networks, but they do not directly address the stochastic formation rates of Borromean triplets in disordered, off-lattice ring systems.

The computational challenge of evaluating triple link invariants and the combinatorial growth of triplet checks complicate direct estimation of formation probabilities in random ring networks.