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Poisson hyperplane tessellations [electronic resource] / Daniel Hug, Rolf Schneider.

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 prop...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Hug, D. (Daniel)
Other Authors: Schneider, Rolf
Format: Electronic eBook
Language:English
Published: Cham : Springer, 2024.
Series:Springer monographs in mathematics.
Subjects:
Poisson processes.
Tessellations (Mathematics)
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.

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