STIT Process and Trees

#### S. Martinez, W. Nagel

2015, v.21, Issue 4, 847-868

ABSTRACT

For the STIT tessellation process, which is becoming one of the reference model in stochastic geometry
for fracture modeling or cell division, we study several constructions in a window of $\RR^\ell$.
A new method is provided which can be efficient for simulations of STIT in any dimension.
Using an appropriate distribution for the dividing hyperplane, we prove that
the cell to be divided can then be chosen equiprobably out of the intersected cells.
Moreover, we supply an exact formula for the transition probabilities
of this Markov process using a representation by binary trees.

Keywords: stochastic geometry, random process of tessellations, STIT tessellation, binary tree, fracture modeling