Continuum Percolation

by Ronald Meester, Rahul Roy

Overview

Many phenomena in physics, chemistry, and biology can be modeled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modeled is made up of individual events that overlap e.g., individual raindrops that eventually make the ground evenly wet. This is a systematic, rigorous account of continuum percolation. The authors treat two models, the Boolean model and the random connection model, in detail, and they discuss related continuum models. Meester and Roy explain all important techniques and methods and apply them to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models.

Product Details

ISBN-13:	9780521062503
Publisher:	Cambridge University Press
Publication date:	05/15/2008
Series:	Cambridge Tracts in Mathematics , #119
Pages:	252
Product dimensions:	5.98(w) x 9.02(h) x 0.59(d)

Table of Contents

Preface; 1. Introduction; 2. Basic methods; 3. Occupancy in Poisson Boolean models; 4. Vacancy in Poisson Boolean models; 5. Distinguishing features of the Poisson Boolean model; 6. The Poisson random-connection model; 7. Models driven by general processes; 8. Other continuum percolation models; References; Index.

Editorial Reviews

"This book is a timely synthesis of the developments in an interesting field. The approach...remains user friendly because of the excellent style and organization. The main arguments are fully explained so as to make the book self-contained. It should be very helpful for new reseachers in the area. Those with interests in related areas such as stochastic geometry and lattice percolation will appreciate having access to such a well-written account of this topic." Matthew D. Penrose, Mathematical Reviews

From the Publisher

Treats the Boolean and the random connection models of continuum percolation, which is used in spatial random processes. Explains the important techniques and methods to obtain results on the existence of phase transitions, the continuity of critical densities with respect to distribution, and other factors. Assumes a familiarity with measure theory and basic probability theory; the simple ergodic theory used should be comprehensible to anyone knowing basic geometry. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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