TY  - BOOK
AU  - Hug,Daniel
AU  - Schneider,Rolf
ED  - SpringerLink (Online service)
TI  - Poisson Hyperplane Tessellations
T2  - Springer Monographs in Mathematics,
SN  - 9783031541049
AV  - QA440-699 
PY  - 2024///
CY  - Cham
PB  - Springer Nature Switzerland, Imprint: Springer
KW  - Geometry
KW  - Stochastic processes
KW  - Stochastic Processes
N1  - - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-031-54104-9
ER  -