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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.
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Lecture Notes in Statistics Edited by S. Fienberg, J. Gani, K. Krickeberg, I. OIkin, and N. Wemmth
87
Jesper M~ller
Lectures On Randolll Voronoi Tessellations
Springer-Verlag
New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest
Jesper M~ller Department of Theoretical Statistics Institute of Mathematics University of Aarhus DK-8000 Aarhus C DENMARK
library of Congress Cataloging-in-Publication Data Mj'jller, Jesper. Lectures on random Voronoi tessellations 1J esper Mj'jller. p. em. -- (Lecture notes in statistics; 87) Includes bibliographical references and index. 1. Voronoi polygons. 2. Spatial analysis (Statistics). I. Title. II. Series: Lecture notes in statistics (Springer-Verlag); v. 87. QA278.2.M64 1994 133.9'01'3 -- dc20 94-248 Printed on acid-free paper. © 1994 Springer-Verlag New York, Inc.
Softcover reprint of the hardcover Ist edition 1994 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Camera ready copy provided by the author.
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ISBN-13: 978-0-387-94264-3 DOl: 10.10071978-1-4612-2652-9
e-ISBN-13: 978-1-4612-2652-9
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