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 . 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}
}