Second-order comparison of three fundamental tessellation models

Autor(en): Redenbach, Claudia
Thaele, Christoph
Stichwörter: 60G55; Mathematics; pair-correlation function; Poisson hyperplane tessellation; Poisson Voronoi tessellation; Primary: 60D05; Secondary: 62M30; Statistics & Probability; STIT tessellation; stochastic geometry; variance of characteristics
Erscheinungsdatum: 2013
Herausgeber: TAYLOR & FRANCIS LTD
Journal: STATISTICS
Volumen: 47
Ausgabe: 2
Startseite: 237
Seitenende: 257
Zusammenfassung: 
We consider three random tessellation models which, due to their analytical tractability, play an important role as reference models for random tessellations: Poisson Voronoi tessellations, Poisson hyperplane tessellations, and STIT tessellations. We present a systematic comparison of second-order properties of these three tessellation models in 2 and 3. If possible, we make use of analytical formulae for the considered characteristics. In cases where explicit formulae are still unknown, the characteristics are studied by simulation.
ISSN: 02331888
DOI: 10.1080/02331888.2011.586458

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