Second-order comparison of three fundamental tessellation models

Abstract

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 ℝ² and ℝ³. 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.

Keywords:

• pair-correlation function
• Poisson hyperplane tessellation
• Poisson Voronoi tessellation
• STIT tessellation
• stochastic geometry
• variance of characteristics

MSC 2000 :

• Primary: 60D05
• 60G55
• Secondary: 62M30

Acknowledgements

The second author was supported by the Swiss National Science Foundation, Grant PP002-114715/1. We would like to thank Lothar Heinrich for helpful comments and stimulating discussions. Moreover, we are grateful to two anonymous referees for their accurate work.