The distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous planar anisotropic STIT tessellations. (English) Zbl 1224.60015

Thäle, Christoph

Commentat. Math. Univ. Carol. 51, No. 3, 503-512 (2010).

The paper yields a new result in the theory of STIT tessellations in stochastic geometry. Its content is a single theorem with proof concerning the distribution of the number of nodes. The main improvement in comparison with previous results is that the assumption of isotropy is relaxed, i.e., the anisotropic case is considered. The formula for the desired distribution involves the Gauss hypergeometric function.

Reviewer: Viktor Beneš (Praha)

MSC:

60D05

Geometric probability and stochastic geometry

Keywords:

random tessellation; hypergeometric function