Estimating the critical threshold for stretched-out hyperbolic random connection models

Abstract

This paper examines the model-dependent asymptotic behaviour of the critical threshold intensity for stretched-out random connection models (RCMs) on hyperbolic spaces. The proof uses lace expansion arguments, but has notable qualitative differences to the Euclidean case in how it evaluates spectral radii. The result is applied to the Boolean disc RCM and a heat kernel RCM.