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Cambridge Tracts in Mathematics #119: Continuum Percolationby Ronald Meester
Synopses & ReviewsPublisher Comments: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.
Book News Annotation: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) Synopsis:This book is the first systematic and rigorous account of continuum percolation. The authors treat two models, the Boolean model and the random connection model, in detail and discuss a number of related continuum models. Where appropriate, they make clear connections between discrete percolation and continuum percolation. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality of certain critical densities, continuity of critical densities with respect to distributions, uniqueness of the unbounded component, covered volume fractions, compression, rarefaction, and so on. The book is selfcontained, assuming familiarity only with measure theory and basic probability theory. The approach makes use of simple ergodic theory, but the underlying geometric ideas are always made clear. Continuum Percolation will appeal to students and researchers in probability and stochastic geometry.
Synopsis:This book presents a unified account of continuum percolation, a spatial random process that can be used to model many natural phenomena. The treatment is selfcontained, assuming only familiarity with measure theory and basic probability theory. It will appeal to students and researchers in probability and stochastic geometry.
Synopsis:A unified treatment of a spatial random process that can be used to model many natural phenomena.
Description:Includes bibliographical references (p. 233235) and index.
Table of Contents1. 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. Some other continuum percolation models.
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