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

Edition	1st ed. 2024.
Publisher	(Cham : Springer Nature Switzerland : Imprint: Springer)
Year	2024
Language	English
Size	XI, 550 p. 27 illus., 26 illus. in color : online resource
Authors	*Hug, Daniel author Schneider, Rolf author SpringerLink (Online service)
Subjects	LCSH:Geometry LCSH:Stochastic processes FREE:Geometry FREE:Stochastic Processes
Notes	- 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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