STIT tessellations are characterized by their surface intensity and by their so-called directional distribution and the metric mean values depend on both parameters.
The paper is structured as follows: After a short introduction on spatial random tessellations we rephrase the definition of STIT tessellations and recall some of their main features which are frequently used later.
STIT tessellations form an interesting class of homogeneous random tessellations, whose cells are not in a face-to-face position and whose properties are mathematically feasible.
Then the STIT tessellations are explained and their basic properties are summarized.
A new model for random tessellations, the so-called STIT tessellations, was introduced in Nagel and Weiss (2005).
Construction: A construction of STIT tessellations in bounded windows was described in all details in Nagel and Weiss (2005) and a global--i.
We will show that the variance (and also other higher moments) of the length of the typical I-segment does not exist for any homogeneous planar STIT tessellation, which shows, that these linear segments are in some sense very long.
This observation is a new feature of STIT tessellations, which can only be observed, when the anisotropic case is studied and this was not investigated until the recent works Mecke (2008) and Thale (2008).
In the present paper the STIT tessellation is briefly described and some properties and quantities are summarized.
Now, the STIT property of a random stationary tessellation means that its distribution is invariant w.
A further model is the so-called STIT tessellation, introduced in Nagel and Weiss (2005).
In the present paper, after a brief description of the STIT model and a review of some key properties, new results for mean values of important parameters are presented.