2013/02/07 by Kiên Kiêu, Katarzyna Adamczyk-Chauvat, Kiêu, Kiên +5
Materials Science · Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Morphological variations and asymmetry #Point processes and geometric inequalities #Quasicrystal Structures and Properties #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1302.1809
openalex publication_date 2013/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.