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

Abstract

Abstract In the first part of this paper we consider a general stationary subcritical cluster model in 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.