Stochastic Geometry: Selected Topics

  • Viktor Beneš
  • Jan Rataj

Table of contents

  1. Front Matter
    Pages i-xi
  2. Pages 1-20
  3. Pages 169-210
  4. Back Matter
    Pages 211-221

About this book

Introduction

Stochastic geometry, based on current developments in geometry, probability and measure theory, makes possible modeling of two- and three-dimensional random objects with interactions as they appear in the microstructure of materials, biological tissues, macroscopically in soil, geological sediments etc. In combination with spatial statistics it is used for the solution of practical problems such as the description of spatial arrangements and the estimation of object characteristics. A related field is stereology, which makes possible inference on the structures, based on lower-dimensional observations. Unfolding problems for particle systems and extremes of particle characteristics are studied. The reader can learn about current developments in stochastic geometry with mathematical rigor on one hand and find applications to real microstructure analysis in natural and material sciences on the other hand.

Keywords

Estimator Poisson process material sciences measure theory modeling point process random measure statistics

Authors and affiliations

  • Viktor Beneš
    • 1
  • Jan Rataj
    • 1
  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPrague

Bibliographic information

  • DOI https://doi.org/10.1007/b129604
  • Copyright Information Springer Science + Business Media, Inc. 2004
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4020-8102-6
  • Online ISBN 978-1-4020-8103-3