Product details:
| ISBN13: | 9783031541032 |
| ISBN10: | 30315410311 |
| Binding: | Hardback |
| No. of pages: | 550 pages |
| Size: | 235x155 mm |
| Language: | English |
| Illustrations: | 1 Illustrations, black & white; 26 Illustrations, color |
| 766 |
Category:
Poisson Hyperplane Tessellations
Series:
Springer Monographs in Mathematics;
Edition number: 2024
Publisher: Springer
Date of Publication: 24 May 2024
Number of Volumes: 1 pieces, Book
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EUR 90.94
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Short description:
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.
Long description:
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.
Table of Contents:
- 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.
