Poisson-Laguerre tessellations

2024/07/01 by Anna Gusakova, Gusakova, Anna, Mathias in Wolde-Lübke +1 · 1 citation
Engineering · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Material Science and Thermodynamics #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2407.01116

Abstract

In this paper we introduce a family of Poisson-Laguerre tessellations in ℝ^d generated by a Poisson point process in ℝ^d× ℝ, whose intensity measure has a density of the form (v,h)↦ f(h)\rm d h \rm d v, where v∈ℝ^d and h∈ℝ, with respect to the Lebesgue measure. We study its sectional properties and show that the ℓ-dimensional section of a Poisson-Laguerre tessellation corresponding to f is an ℓ-dimensional Poisson-Laguerre tessellation corresponding to f_ℓ, which is up to a constant a fractional integral of f of order (d-ℓ)/2. Further we derive an explicit representation for the distribution of the volume weighted typical cell of the dual Poisson-Laguerre tessellation in terms of fractional integrals and derivatives of f.

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