Aggregate and fractal tessellations

Tchoumatchenko, Konstantin and Zuev, Sergei (2001) Aggregate and fractal tessellations. Probability Theory and Related Fields, 121 (2). pp. 198-218. ISSN 0178-8051 (https://doi.org/10.1007/PL00008802)

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Abstract

Consider a sequence of stationary tessellations {‹n}, n=0,1,..., of  d consisting of cells {Cn(xin)}with the nuclei {xin}. An aggregate cell of level one, C01(xi0), is the result of merging the cells of ‹1 whose nuclei lie in C0(xi0). An aggregate tessellation ‹0n consists of the aggregate cells of level n, C0n(xi0), defined recursively by merging those cells of ‹n whose nuclei lie in Cnm1(xi0). We find an expression for the probability for a point to belong to atypical aggregate cell, and obtain bounds for the rate of itsexpansion. We give necessary conditions for the limittessellation to exist as nMX and provide upperbounds for the Hausdorff dimension of its fractal boundary and forthe spherical contact distribution function in the case ofPoisson-Voronoi tessellations {‹n}.

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• Item metadata

  Item type:	Article
  ID code:	4605
  Dates:	Date Event 31 October 2001 Published
  Subjects:	Science > Mathematics > Probabilities. Mathematical statistics
  Department:	Faculty of Science > Mathematics and Statistics > Statistics and Modelling Science
  Depositing user:	Strathprints Administrator
  Date deposited:	06 Nov 2007
  Last modified:	12 Dec 2024 02:08
  URI:	https://strathprints.strath.ac.uk/id/eprint/4605