LIMIT THEOREMS FOR ITERATION STABLE TESSELLATIONS

• 成果类型: Article
• 署名作者: Schreiber, Tomasz; Thaele, Christoph
• 署名单位: Nicolaus Copernicus University; University Osnabruck
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP718
• 发表日期: 2013
• 页码: 2261-2278
• 关键词: 2nd-order properties; stationary; CONSTRUCTION; cells

摘要

The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in 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 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.