Continuum Percolation (Cambridge Tracts in Mathematics)

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9780521062503: Continuum Percolation (Cambridge Tracts in Mathematics)
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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.

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This book presents a unified account of current knowledge of the theory of continuum percolation, a kind of spatial random process that can be used to model many natural phenomena. The treatment is systematic and rigorous. Two models of continuum percolation are treated in detail and related models are discussed. All important techniques and methods are explained and applied. This self-contained book, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry.

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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.

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9780521475044: Continuum Percolation (Cambridge Tracts in Mathematics)

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Publisher: Cambridge University Press, 1996
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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2008. Paperback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****. Many phenomena in physics, chemistry, and biology can be modelled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modelled is made up of individual events that overlap, for example, the way individual raindrops eventually make the ground evenly wet. This is a systematic rigorous account of continuum percolation. Two models, the Boolean model and the random connection model, are treated in detail, and related continuum models are discussed. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models. This self-contained treatment, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry. Seller Inventory # AAV9780521062503

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2008. Paperback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****.Many phenomena in physics, chemistry, and biology can be modelled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modelled is made up of individual events that overlap, for example, the way individual raindrops eventually make the ground evenly wet. This is a systematic rigorous account of continuum percolation. Two models, the Boolean model and the random connection model, are treated in detail, and related continuum models are discussed. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models. This self-contained treatment, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry. Seller Inventory # AAV9780521062503

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Book Description Cambridge University Press. Paperback. Condition: New. 252 pages. Dimensions: 8.9in. x 6.0in. x 0.9in.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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Seller Inventory # 9780521062503

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