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hypergeometric function; iteration/nesting; random tessellation; segments; stochastic geometry; stochastic stability
A result about the distribution of the number of nodes in the relative interior of the typical I-segment in homogeneous and isotropic random tessellations stable under iteration (STIT tessellations) is extended to the anisotropic case using recent findings from Schreiber/Thäle, Typical geometry, second-order properties and central limit theory for iteration stable tessellations, arXiv:1001.0990 [math.PR] (2010). Moreover a new expression for the values of this probability distribution is presented in terms of the Gauss hypergeometric function ${_2F_1}$.
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