On the Ornstein-Zernike equation for stationary cluster processes and the random connection model

Abstract

In the first part of this paper we consider a general stationary subcritical cluster model in ${\mathbb{R}}^d$. The associated pair-connectedness function can be defined in terms of two-point Palm probabilities of the underlying point process. Using Palm calculus and Fourier theory we solve the Ornstein-Zernike equation (OZE) under quite general distributional assumptions. In the second part of the paper we discuss the analytic and combinatorial properties of the OZE-solution in the special case of a Poisson driven random connection model.