Expansion of the Critical Intensity for the Random Connection Model

Abstract

We derive an asymptotic expansion for the critical percolation density of the random connection model as the dimension of the encapsulating space tends to infinity. We calculate rigorously the first expansion terms for the Gilbert disk model, the hyper-cubic model, the Gaussian connection kernel, and a coordinate-wise Cauchy kernel.

43 pages, 7 figures

References in corpus (1)

• Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk