Second-order comparison of three fundamental tessellation models

作者：Redenbach Claudia^*; Thaele Christoph

来源：Statistics, 2013, 47(2): 237-257.

DOI：10.1080/02331888.2011.586458

• pair-correlation function
• Poisson hyperplane tessellation
• Poisson Voronoi tessellation
• STIT tessellation
• stochastic geometry
• variance of characteristics
• Primary: 60D05
• 60G55
• Secondary: 62M30

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.

• 出版日期2013-4-1