### Abstract

Language | English |
---|---|

Pages | 198-218 |

Number of pages | 20 |

Journal | Probability Theory and Related Fields |

Volume | 121 |

Issue number | 2 |

DOIs | |

Publication status | Published - 31 Oct 2001 |

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### Keywords

- probability
- voronoï tessellation
- pProbability distribution
- telecommunications
- poisson process
- fractal

### Cite this

*Probability Theory and Related Fields*,

*121*(2), 198-218. https://doi.org/10.1007/PL00008802

}

*Probability Theory and Related Fields*, vol. 121, no. 2, pp. 198-218. https://doi.org/10.1007/PL00008802

**Aggregate and fractal tessellations.** / Tchoumatchenko, Konstantin; Zuev, Sergei.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Aggregate and fractal tessellations

AU - Tchoumatchenko, Konstantin

AU - Zuev, Sergei

PY - 2001/10/31

Y1 - 2001/10/31

N2 - 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}.

AB - 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}.

KW - probability

KW - voronoï tessellation

KW - pProbability distribution

KW - telecommunications

KW - poisson process

KW - fractal

U2 - 10.1007/PL00008802

DO - 10.1007/PL00008802

M3 - Article

VL - 121

SP - 198

EP - 218

JO - Probability Theory and Related Fields

T2 - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 2

ER -