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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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https://hal.archives-ouvertes.fr/hal-00785980
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Submitted on : Wednesday, March 27, 2013 - 9:16:03 AM
Last modification on : Wednesday, March 23, 2022 - 3:50:06 PM
Long-term archiving on: : Sunday, April 2, 2017 - 8:58:19 PM

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  • HAL Id : hal-00785980, version 3
  • ARXIV : 1302.1809

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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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