Limit theorems for iteration stable tessellations

• Tomasz Schreiber ^[1] ; Christoph Thäle ^[2]
  1. [1] Nicolaus Copernicus University

     Nicolaus Copernicus University

     Toruń, Polonia

     
  2. [2] University of Osnabrück

     University of Osnabrück

     Kreisfreie Stadt Osnabrück, Alemania

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 3, 2, 2013, págs. 2261-2278
• Idioma: inglés
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• Resumen

  • The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in Rd, 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 process induced a by STIT tessellation 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 nonnormal limit showing up in all higher space dimensions.