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Poisson hyperplane tessellations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Poisson hyperplane tessellationsby Daniel Hug, Rolf Schneider.
Author:	Hug, Daniel.
other author:	Schneider, Rolf.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xi, 550 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Poisson processes.
Online resource:	https://doi.org/10.1007/978-3-031-54104-9
ISBN:	9783031541049$q(electronic bk.)

Poisson hyperplane tessellations
Hug, Daniel.

Poisson hyperplane tessellations[electronic resource] /by Daniel Hug, Rolf Schneider. - Cham :Springer Nature Switzerland :2024. - xi, 550 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

- 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.

ISBN: 9783031541049$q(electronic bk.)

Standard No.: 10.1007/978-3-031-54104-9doiSubjects--Topical Terms:

191620
Poisson processes.

LC Class. No.: QA274.42

Dewey Class. No.: 519.24

Poisson hyperplane tessellations
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505 0 $a - 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.
520 $a 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.
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