Geometry of Iteration Stable Tessellations: Connection with Poisson Hyperplanes

Details Geometry of Iteration Stable Tessellations: Connection with Poisson Hyperplanes Geometry of Iteration Stable Tessellations: Connection with Poisson Hyperplanes

2011-03-21

arxiv.org/abs/1103.3958v1

Mathematics

Probability

Scientific paper

Since the seminal work \cite{NW03,NW05} the iteration stable (STIT) tessellations have attracted considerable interest in stochastic geometry as a natural and flexible, yet analytically tractable model for hierarchical spatial cell-splitting and crack-formation processes considered in stochastic geometry. We provide in this paper a fundamental link between typical characteristics of STIT tessellations and those of suitable mixtures of Poisson hyperplane tessellations using martingale techniques and general theory of pure jump Markov processes. As applications, new mean values and new distributional results for STIT tessellations are obtained.

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