Exponential decay for the random connection model using asymptotic transitivity
Abstract
We prove that the probability the cluster of the origin in a subcritical Poisson random connection model (RCM) has size at least n decays exponentially as n increases, under minimal assumptions. We extend a recent method of Vanneuville from Bernoulli percolation on vertex-transitive graphs to the RCM, where the vertex set has little structure. The key idea is that the subcritical RCM can be constructed by site percolation on a high-intensity RCM. The latter RCM becomes “almost vertex-transitive” at very high intensities. We obtain the result for connection functions with unbounded support, a setting in which it was not previously known.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Theoretical and Computational Physics
Random Matrices and Applications
Publication details
- Journal / source
- Electronic Journal of Probability
- Volume
- 31
- Issue
- none
- Pages
- 1–16
- Publication date
- 1 January 2026
- Language
- EN