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Poisson Hyperplane Tessellations / by Daniel Hug, Rolf Schneider
(Springer Monographs in Mathematics. ISSN:21969922)

1st ed. 2024.
出版者 (Cham : Springer Nature Switzerland : Imprint: Springer)
出版年 2024
本文言語 英語
大きさ XI, 550 p. 27 illus., 26 illus. in color : online resource
著者標目 *Hug, Daniel author
Schneider, Rolf author
SpringerLink (Online service)
件 名 LCSH:Geometry
LCSH:Stochastic processes
FREE:Geometry
FREE:Stochastic Processes
一般注記 - 1 Notation -- 2 Hyperplane and particle processes -- 3 Distribution-independent density relations -- 4 Poisson hyperplane processes -- 5 Auxiliary functionals and bodies -- 6 Zero cell and typical cell -- 7 Mixing and ergodicity -- 8 Observations inside a window -- 9 Central limit theorems -- 10 Palm distributions and related constructions -- 11 Typical faces and weighted faces -- 12 Large cells and faces -- 13 Cells with a given number of facets -- 14 Small cells -- 15 The K-cell under increasing intensities -- 16 Isotropic zero cells -- 17 Functionals of Poisson processes and applications -- 18 Appendix: Some auxiliary results
This book is the first comprehensive presentation of a central topic of stochastic geometry: random mosaics that are generated by Poisson processes of hyperplanes. It thus connects a basic notion from probability theory, Poisson processes, with a fundamental object of geometry. The independence properties of Poisson processes and the long-range influence of hyperplanes lead to a wide range of phenomena which are of interest from both a geometric and a probabilistic point of view. A Poisson hyperplane tessellation generates many random polytopes, also a much-studied object of stochastic geometry. The book offers a variety of different perspectives and covers in detail all aspects studied in the original literature. The work will be useful to graduate students (advanced students in a Master program, PhD students), and professional mathematicians. The book can also serve as a reference for researchers in fields of physics, computer science, economics or engineering
HTTP:URL=https://doi.org/10.1007/978-3-031-54104-9
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Springer eBooks 9783031541049
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データ種別 電子ブック
分 類 LCC:QA440-699
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書誌ID 4001111997
ISBN 9783031541049

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