CRACK STIT TESSELLATIONS - EXISTENCE AND UNIQUENESS OF TESSELLATIONS THAT ARE STABLE WITH RESPECT TO ITERATIONS

摘要

The paper defines the class of Crack STIT spatially homogeneous tessellations as particular models for a number of applications. A summary of essential properties is given, namely the stochastic stability with respect to iteration (nesting) of tessellations and the distribution of the interior of the typical cell, which coincides with that one of the Poisson hyperplane tessellation. The Crack STIT tessellations are the only ones which are stable with respect to iteration. Intensities and geometric features for planar Crack STIT tessellations are considered.