ENGLISH

Poisson Hyperplane Tessellations

By Rolf Schneider , Daniel Hug

Book information

Publisher
Springer Nature Switzerland
Year
2024
ISBN
9783031541032, 9783031541049
DOI
10.1007/978-3-031-54104-9
ISSN
2196-9922
Language
english
Format
PDF
Filesize
15 MB (15743389 bytes)
Series
Springer Monographs in Mathematics
Edition
1
Pages
550\550
Orientation
yes
Paginated
yes
Scanned
portrait
Time added
2024-05-25 14:04:54
Central Limit TheoremsErgodicityHyperplane ProcessesMixingPalm DistributionsParticle ProcessesPoint Processes

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. - The first comprehensive treatment of Poisson hyperplane tessellations - Considers all aspects of a beautiful and accessible subject - Proceeds from elementary foundations to most recent active research

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