Institute of Mathematics, University of Osnabrüuck, Osnabrüuck, Germany
E-mail address: email@example.com
(Received March 15, 2010; Accepted March 8, 2011)
Abstract. Formulas for the joint distribution of direction and length of the typical K- and J -segment in a planar, homogeneous, anisotropic, random tessellations that are stable under iteration (so-called STIT tessellations) are derived. They were announced in Thäle (2009), supplement the results from Mecke (2009) and Mecke et al. (2007) and complete the picture concerning length distributions of segments in the planar case.
Keywords: Length Distribution, Iteration/Nesting, Random Tessellation, STIT Tessellation, Stochastic Geometry