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Lectures on Random Voronoi Tessellations

  • Book
  • © 1994

Overview

Authors:
  1. Jesper Møller

    1. Department of Theoretical Statistics Institute of Mathematics, University of Aarhus, Aarhus C, Denmark

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Part of the book series: Lecture Notes in Statistics (LNS, volume 87)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction and background

    • Jesper Møller
    Pages 1-14

  3. Geometrical properties and other background material

    • Jesper Møller
    Pages 15-42

  4. Stationary Voronoi tessellations

    • Jesper Møller
    Pages 43-82

  5. Poisson-Voronoi tessellations

    • Jesper Møller
    Pages 83-124

  6. Back Matter

    Pages 125-137
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Keywords

About this book

Tessellations are subdivisions of d-dimensional space into non-overlapping "cells". Voronoi tessellations are produced by first considering a set of points (known as nuclei) in d-space, and then defining cells as the set of points which are closest to each nuclei. A random Voronoi tessellation is produced by supposing that the location of each nuclei is determined by some random process. They provide models for many natural phenomena as diverse as the growth of crystals, the territories of animals, the development of regional market areas, and in subjects such as computational geometry and astrophysics. This volume provides an introduction to random Voronoi tessellations by presenting a survey of the main known results and the directions in which research is proceeding. Throughout the volume, mathematical and rigorous proofs are given making this essentially a self-contained account in which no background knowledge of the subject is assumed.

Authors and Affiliations

  • Department of Theoretical Statistics Institute of Mathematics, University of Aarhus, Aarhus C, Denmark

    Jesper Møller

Bibliographic Information

  • Book Title: Lectures on Random Voronoi Tessellations

  • Authors: Jesper Møller

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-2652-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1994

  • Softcover ISBN: 978-0-387-94264-3Published: 08 April 1994

  • eBook ISBN: 978-1-4612-2652-9Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: VIII, 134

  • Topics: Probability Theory and Stochastic Processes

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