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Title: Exponential moments for planar tessellations
Authors: Tóbiás, AndrásJahnel, Benedikt
Publishers Version: https://doi.org/10.20347/WIAS.PREPRINT.2572
Issue Date: 2019
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2572, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: In this paper we show existence of all exponential moments for the total edge length in a unit disc for a family of planar tessellations based on Poisson point processes. Apart from classical such tessellations like the PoissonVoronoi, PoissonDelaunay and Poisson line tessellation, we also treat the JohnsonMehl tessellation, Manhattan grids, nested versions and Palm versions. As part of our proofs, for some planar tessellations, we also derive existence of exponential moments for the number of cells and the number of edges intersecting the unit disk.
Keywords: Poisson–Voronoi tessellation; Poisson–Delaunay tessellation; Poisson line tessellation; Johnson–Mehl tessellation; Manhattan grid; Cox–Voronoi tessellation; nested tessellation; iterated tessellation; exponential moments; total edge length; number of cells; number of edges; Palm calculus
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
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Appears in Collections:Mathematik



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