English

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

Probability 2016-07-12 v1

Abstract

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

Keywords

Cite

@article{arxiv.1607.02962,
  title  = {On the Ornstein-Zernike equation for stationary cluster processes and the random connection model},
  author = {Günter Last and Sebastian Ziesche},
  journal= {arXiv preprint arXiv:1607.02962},
  year   = {2016}
}