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

Günter Last; Sebastian Ziesche

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arXiv · 1607.02962

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

Günter Last·Sebastian Ziesche

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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.

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Günter Last, Sebastian Ziesche. 2016-07-11. On the Ornstein-Zernike equation for stationary cluster processes and the random connection model. https://arxiv.org/abs/1607.02962

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