MOMENTS OF THE LENGTH OF LINE SEGMENTS IN HOMOGENEOUS PLANAR STIT TESSELLATIONS

Abstract

Homogeneous planar tessellations stable under iteration (STIT tessellations) are considered. Using recent results about the joint distribution of direction and length of the typical I-, K- and J-segment we prove closed formulas for the first, second and higher moments of the length of these segments given their direction. This especially leads to themean values and variances of these quantities andmean value relations as well as general moment relationships. Moreover, the relation between these mean values and certain conditional mean values (and also higher moments) is discussed. The results are also illustrated for several examples.

Keywords

• conditional distribution
• iteration (nesting)
• linear segments
• mean value relation
• moments
• random tessellation
• stability
• stochastic geometry