Cells with many facets in a Poisson hyperplane tessellation
DC Element | Wert | Sprache |
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dc.contributor.author | Bonnet, Gilles | |
dc.contributor.author | Calka, Pierre | |
dc.contributor.author | Reitzner, Matthias | |
dc.date.accessioned | 2021-12-23T16:18:09Z | - |
dc.date.available | 2021-12-23T16:18:09Z | - |
dc.date.issued | 2018 | |
dc.identifier.issn | 00018708 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/12566 | - |
dc.description.abstract | Let Z be the typical cell of a stationary Poisson hyperplane tessellation in R-d. The distribution of the number of facets f (Z) of the typical cell is investigated. It is shown, that under a well-spread condition on the directional distribution, the quantity n 2/d-1 n root P(f(Z)=n is bounded from above and frombelow. When f(Z) is large, the isoperimetric ratio of Z is bounded away from zero with high probability. These results rely on one hand on the Complementary Theorem which provides a precise decomposition of the distribution of Z and on the other hand on several geometric estimates related to the approximation of polytopes by polytopes with fewer facets. From the asymptotics of the distribution of f (Z), tail estimates for the so-called phi content of Z are derived as well as results on the conditional distribution of Z when its phi. content is large. (C) 2017 Elsevier Inc. All rights reserved. | |
dc.description.sponsorship | DFGGerman Research Foundation (DFG)European Commission [GK 1916]; Supported by the DFG (project GK 1916). | |
dc.language.iso | en | |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | |
dc.relation.ispartof | ADVANCES IN MATHEMATICS | |
dc.subject | Complementary Theorem | |
dc.subject | DG Kendall's problem | |
dc.subject | Directional distribution | |
dc.subject | Mathematics | |
dc.subject | Poisson hyperplane tessellation | |
dc.subject | Random polytopes | |
dc.subject | SHAPE | |
dc.subject | Typical cell | |
dc.title | Cells with many facets in a Poisson hyperplane tessellation | |
dc.type | journal article | |
dc.identifier.doi | 10.1016/j.aim.2017.11.016 | |
dc.identifier.isi | ISI:000418780700006 | |
dc.description.volume | 324 | |
dc.description.startpage | 203 | |
dc.description.endpage | 240 | |
dc.contributor.orcid | 0000-0003-4161-4124 | |
dc.contributor.researcherid | AAR-4190-2021 | |
dc.identifier.eissn | 10902082 | |
dc.publisher.place | 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA | |
dcterms.isPartOf.abbreviation | Adv. Math. | |
dcterms.oaStatus | Green Submitted | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | ReMa759 | - |
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