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

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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2017021715545
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dc.contributor.advisorProf. Dr. Matthias Reitzner
dc.creatorBonnet, Gilles
dc.date.accessioned2017-02-17T08:06:57Z
dc.date.available2017-02-17T08:06:57Z
dc.date.issued2017-02-17T08:06:57Z
dc.identifier.urihttps://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2017021715545-
dc.description.abstractWe 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.eng
dc.rightsNamensnennung - Weitergabe unter gleichen Bedingungen 3.0 Unported-
dc.rights.urihttp://creativecommons.org/licenses/by-sa/3.0/-
dc.subjectStochastic Geometryeng
dc.subjectConvex Geometryeng
dc.subjecttessellationeng
dc.subjectmosaiceng
dc.subjectrandom tessellationeng
dc.subjectPoisson hyperplane tessellationeng
dc.subjectZero celleng
dc.subjectTypical celleng
dc.subjectAsymptotic probabilitieseng
dc.subjectD.G. Kendall's problemeng
dc.subjectComplementary theoremeng
dc.subjectpolytopal approximationeng
dc.subjectdelta-neteng
dc.subjectelongated convex bodieseng
dc.subjectgeometric integral transformation formulaeeng
dc.subjectfacetseng
dc.subjectPhi-Contenteng
dc.subjectcentereng
dc.subjectshapeeng
dc.subjecttail distributioneng
dc.subjectsmall cellseng
dc.subject.ddc510 - Mathematik
dc.titlePoisson hyperplane tessellation: Asymptotic probabilities of the zero and typical cellseng
dc.typeDissertation oder Habilitation [doctoralThesis]-
thesis.locationOsnabrück-
thesis.institutionUniversität-
thesis.typeDissertation [thesis.doctoral]-
thesis.date2016-12-09-
dc.contributor.refereeProf. Dr. Ilya Molchanov
dc.subject.msc60D05 - Geometric probability, stochastic geometry, random sets
vCard.ORGFB6
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