Poisson hyperplane tessellations / Daniel Hug, Rolf Schneider.

Format:

Book

Author/Creator:

Hug, D. (Daniel), author.

Schneider, Rolf, 1940- author.

Series:

Springer monographs in mathematics. 1439-7382

Springer monographs in mathematics ; 1439-7382

Language:

English

Subjects (All):

Poisson processes.

Tessellations (Mathematics).

Physical Description:

xi, 550 pages : illustrations (some color) ; 24 cm.

Place of Publication:

Cham : Springer, [2024]

Summary:

"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"--Back cover.

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.

Notes:

Includes bibliographical references and indexes.

ISBN:

9783031541032

3031541030

OCLC:

1417196084