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}.
Original language | English |
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Pages (from-to) | 198-218 |
Number of pages | 20 |
Journal | Probability Theory and Related Fields |
Volume | 121 |
Issue number | 2 |
DOIs | |
Publication status | Published - 31 Oct 2001 |
Keywords
- probability
- voronoï tessellation
- pProbability distribution
- telecommunications
- poisson process
- fractal