Poisson polyhedra in high dimensions
DC Element | Wert | Sprache |
---|---|---|
dc.contributor.author | Hoerrmann, Julia | |
dc.contributor.author | Hug, Daniel | |
dc.contributor.author | Reitzner, Matthias | |
dc.contributor.author | Thaele, Christoph | |
dc.date.accessioned | 2021-12-23T16:17:06Z | - |
dc.date.available | 2021-12-23T16:17:06Z | - |
dc.date.issued | 2015 | |
dc.identifier.issn | 00018708 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/12199 | - |
dc.description.abstract | The zero cell of a parametric class of random hyperplane tessellations depending on a distance exponent and an intensity parameter is investigated, as the space dimension tends to infinity. The model includes the zero cell of stationary and isotropic Poisson hyperplane tessellations as well as the typical cell of a stationary Poisson Voronoi tessellation as special cases. It is shown that asymptotically in the space dimension, with overwhelming probability these cells satisfy the hyperplane conjecture, if the distance exponent and the intensity parameter are suitably chosen dimension-dependent functions. Also the high dimensional limits of the mean number of faces are explored and the asymptotic behaviour of an isoperimetric ratio is analysed. In the background are new identities linking the f-vector of the zero cell to certain dual intrinsic volumes. (C) 2015 Elsevier Inc. All rights reserved. | |
dc.description.sponsorship | German Research Foundation (DFG) via the Research Group FOR 1548 ``Geometry and Physics of Spatial Random Systems''German Research Foundation (DFG); German Research Foundation (DFG)German Research Foundation (DFG) [SFB-TR 12]; The authors would like to thank an anonymous referee for his useful comments which helped to improve the manuscript. JH and DH have been supported by the German Research Foundation (DFG) via the Research Group FOR 1548 ``Geometry and Physics of Spatial Random Systems''. CT has been supported by the German Research Foundation (DFG) via SFB-TR 12 ``Symmetries and Universality in Mesoscopic Systems''. | |
dc.language.iso | en | |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | |
dc.relation.ispartof | ADVANCES IN MATHEMATICS | |
dc.subject | BODIES | |
dc.subject | Dual intrinsic volume | |
dc.subject | f-Vector | |
dc.subject | High dimensional polyhedra | |
dc.subject | HYPERPLANE CONJECTURE | |
dc.subject | Hyperplane tessellation | |
dc.subject | Isoperimetric ratio | |
dc.subject | ISOTROPY CONSTANT | |
dc.subject | Mathematics | |
dc.subject | Poisson Voronoi tessellation | |
dc.subject | Random polyhedron | |
dc.subject | SPACES | |
dc.subject | VOLUME | |
dc.subject | Zero cell | |
dc.title | Poisson polyhedra in high dimensions | |
dc.type | journal article | |
dc.identifier.doi | 10.1016/j.aim.2015.03.025 | |
dc.identifier.isi | ISI:000358460000001 | |
dc.description.volume | 281 | |
dc.description.startpage | 1 | |
dc.description.endpage | 39 | |
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 | Bronze | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | ReMa759 | - |
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geprüft am 23.05.2024