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Random Laguerre tessellations
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A systematic study of random Laguerre tessellations, weighted generalisations of the well-known Voronoi tessellations, is presented. We prove that every normal tessellation with convex cells in dimension three and higher is a Laguerre tessellation. Tessellations generated by stationary marked Poisson processes are then studied in detail. For these tessellations, we obtain integral formulae for geometric characteristics and densities of the typical
k
-faces. We present a formula for the linear contact distribution function and prove various limit results for convergence of Laguerre to Poisson-Voronoi tessellations. The obtained integral formulae are subsequently evaluated numerically for the planar case, demonstrating their applicability for practical purposes.
Cambridge University Press (CUP)
Title: Random Laguerre tessellations
Description:
A systematic study of random Laguerre tessellations, weighted generalisations of the well-known Voronoi tessellations, is presented.
We prove that every normal tessellation with convex cells in dimension three and higher is a Laguerre tessellation.
Tessellations generated by stationary marked Poisson processes are then studied in detail.
For these tessellations, we obtain integral formulae for geometric characteristics and densities of the typical
k
-faces.
We present a formula for the linear contact distribution function and prove various limit results for convergence of Laguerre to Poisson-Voronoi tessellations.
The obtained integral formulae are subsequently evaluated numerically for the planar case, demonstrating their applicability for practical purposes.
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