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Preprints, Working Papers, ... Year : 2013

A completely random T-tessellation model and Gibbsian extensions

Abstract

In their 1993 paper, Arak, Clifford and Surgailis discussed a new model of random planar graph. As a particular case, that model yields tessellations with only T-vertices (T-tessellations). Using a similar approach involving Poisson lines, a new model of random T-tessellations is proposed. Campbell measures, Papangelou kernels and Georgii-Nguyen-Zessin formulae are translated from point process theory to random T-tessellations. It is shown that the new model shows properties similar to the Poisson point process and can therefore be considered as a completely random T-tessellation. Gibbs variants are introduced leading to models of random T-tessellations where selected features are controlled. Gibbs random T-tessellations are expected to better represent observed tessellations. As numerical experiments are a key tool for investigating Gibbs models, we derive a simulation algorithm of the Metropolis-Hastings-Green family.
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Dates and versions

hal-00785980 , version 1 (07-02-2013)
hal-00785980 , version 2 (22-02-2013)
hal-00785980 , version 3 (27-03-2013)

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Kiên Kiêu, Katarzyna Adamczyk-Chauvat, Hervé Monod, Radu S. Stoica. A completely random T-tessellation model and Gibbsian extensions. 2013. ⟨hal-00785980v3⟩
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