03561nam a22005295i 4500 978-3-031-54104-9 DE-He213 20251030112055.0 cr nn 008mamaa 240523s2024 sz | s |||| 0|eng d 9783031541049 978-3-031-54104-9 10.1007/978-3-031-54104-9 doi QA440-699 PBM bicssc MAT012000 bisacsh PBM thema Hug, Daniel. author. aut http://id.loc.gov/vocabulary/relators/aut 77285 Poisson Hyperplane Tessellations [electronic resource] / by Daniel Hug, Rolf Schneider. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XI, 550 p. 27 illus., 26 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Monographs in Mathematics, 2196-9922 - 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. Geometry. 68763 Stochastic processes. 76770 Geometry. 68763 Stochastic Processes. 76770 Schneider, Rolf. author. aut http://id.loc.gov/vocabulary/relators/aut 77286 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031541032 Printed edition: 9783031541056 Printed edition: 9783031541063 Springer Monographs in Mathematics, 2196-9922 73001 https://doi.org/10.1007/978-3-031-54104-9 ZDB-2-SMA ZDB-2-SXMS 60061 60061