Poisson Hyperplane Tessellations - Hug, Daniel; Schneider, Rolf; - Prospero Internet Bookshop

Poisson Hyperplane Tessellations
 
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

 
Edition number: 2024
Publisher: Springer
Date of Publication:
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.