Tchoumatchenko, K. and Zuev, S. (2001) *Aggregate and fractal tessellations.* Probability Theory and Related Fields, 121 (2). pp. 198-218. ISSN 0178-8051

## Abstract

Consider a sequence of stationary tessellations {‹n}, n=0,1,..., of Â 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}.

Item type: | Article |

ID code: | 4605 |

Keywords: | probability, voronoï tessellation, pProbability distribution, telecommunications, poisson process, fractal, Probabilities. Mathematical statistics, Analysis, Statistics and Probability, Statistics, Probability and Uncertainty |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics > Statistics and Modelling Science |

Related URLs: | |

Depositing user: | Strathprints Administrator |

Date Deposited: | 06 Nov 2007 |

Last modified: | 05 Sep 2014 13:13 |

URI: | http://strathprints.strath.ac.uk/id/eprint/4605 |
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