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25 Remote Warehouse Physics- General

Cambridge Tracts in Mathematics #119: Continuum Percolation

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Cambridge Tracts in Mathematics #119: Continuum Percolation Cover

 

Synopses & Reviews

Publisher 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 self-contained, 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 self-contained, 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. 233-235) and index.

Table of Contents

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. Some other continuum percolation models.

Product Details

ISBN:
9780521475044
Editor:
Bollobas, B.
Editor:
Roy, Rahul
With:
Roy, Rahul
Editor:
Bollobas, Bela
Editor:
Fulton, W.
Editor:
Bollobas, B.
Author:
Katok, A.
Author:
Bollobas, B.
Author:
Roy, Rahul
Author:
Fulton, W.
Author:
Meester, Ronald
Author:
Sarnak, P.
Author:
Kirwan, F.
Publisher:
Cambridge University Press
Location:
Cambridge ;
Subject:
Physics
Subject:
Differential Equations
Subject:
Statistics
Subject:
Probability
Subject:
Stochastic processes
Subject:
Mathematical Physics
Subject:
Percolation (Statistical physics)
Subject:
Percolation
Subject:
Probability & Statistics - General
Subject:
Physics-General
Edition Description:
Hardcover
Series:
Cambridge Tracts in Mathematics (Hardcover)
Series Volume:
L119
Publication Date:
20041031
Binding:
Hardcover
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
26 line diagrams
Pages:
252
Dimensions:
9.18x6.21x.89 in. 1.17 lbs.

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Related Subjects

Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics
Science and Mathematics » Physics » General

Cambridge Tracts in Mathematics #119: Continuum Percolation New Hardcover
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$161.50 In Stock
Product details 252 pages Cambridge University Press - English 9780521475044 Reviews:
"Synopsis" by , 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 self-contained, 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" by , 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 self-contained, assuming only familiarity with measure theory and basic probability theory. It will appeal to students and researchers in probability and stochastic geometry.
"Synopsis" by , A unified treatment of a spatial random process that can be used to model many natural phenomena.
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