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

2016/07/11 by Last, Günter, Ziesche, Sebastian · 2 citations
#60G55 (Secondary) #60K35 (Primary) 60D05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1607.02962

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.

Cited by

• On strong sharp phase transition in the random connection model
• Crossings and diffusion in Poisson driven marked random connection models

Related

• Near-critical Ornstein--Zernike theory for the planar random-cluster model
• On strong sharp phase transition in the random connection model
• The random connection model and functions of edge-marked Poisson processes: second order properties and normal approximation
• Recurrence versus Transience for Weight-Dependent Random Connection Models
• Exponential decay for the random connection model using asymptotic transitivity