Limit Theorems for Iteration Stable Tessellations

Details Limit Theorems for Iteration Stable Tessellations Limit Theorems for Iteration Stable Tessellations

2011-03-21

arxiv.org/abs/1103.3960v1

Mathematics

Probability

Scientific paper

The intent of this paper is to describe large scale asymptotic geometry of STIT tessellations in ${\Bbb R}^d$, which form a rather new, rich and flexible class of random tessellations considered in stochastic geometry. For this purpose, martingale tools are combined with second-order formulas proved earlier to establish limit theorems for STIT tessellations. More precisely, a Gaussian functional central limit theorem for the surface increment processes induced by STIT tessellations relative to an initial time moment is shown. As second main result, a central limit theorem for the total edge length/facet surface is obtained, with a normal limit distribution in the planar case and, most interestingly, with a non-normal limit showing up in all higher space dimensions -- including the practically relevant spatial case.

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