Poisson hyperplane tessellation: Asymptotic probabilities of the zero and typical cells

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Title: Poisson hyperplane tessellation: Asymptotic probabilities of the zero and typical cells
Authors: Bonnet, Gilles
Thesis advisor: Prof. Dr. Matthias Reitzner
Thesis referee: Prof. Dr. Ilya Molchanov
Abstract: We consider the distribution of the zero and typical cells of a (homogeneous) Poisson hyperplane tessellation. We give a direct proof adapted to our setting of the well known Complementary Theorem. We provide sharp bounds for the tail distribution of the number of facets. We also improve existing bounds for the tail distribution of size measurements of the cells, such as the volume or the mean width. We improve known results about the generalised D.G. Kendall's problem, which asks about the shape of large cells. We also show that cells with many facets cannot be close to a lower dimensional convex body. We tacle the much less study problem of the number of facets and the shape of small cells. In order to obtain the results above we also develop some purely geometric tools, in particular we give new results concerning the polytopal approximation of an elongated convex body.
URL: https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2017021715545
Subject Keywords: Stochastic Geometry; Convex Geometry; tessellation; mosaic; random tessellation; Poisson hyperplane tessellation; Zero cell; Typical cell; Asymptotic probabilities; D.G. Kendall's problem; Complementary theorem; polytopal approximation; delta-net; elongated convex bodies; geometric integral transformation formulae; facets; Phi-Content; center; shape; tail distribution; small cells
Issue Date: 17-Feb-2017
License name: Namensnennung - Weitergabe unter gleichen Bedingungen 3.0 Unported
License url: http://creativecommons.org/licenses/by-sa/3.0/
Type of publication: Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:FB06 - E-Dissertationen

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