%0 Journal Article
%T A completely random T-tessellation model and Gibbsian extensions
%A Ki¨ºn Ki¨ºu
%A Katarzyna Adamczyk-Chauvat
%A Herv¨¦ Monod
%A Radu S. Stoica
%J Statistics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1302.1809v3