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  1. Home
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  3. Continuum Percolation
  • Cited by 643
Publisher:
Cambridge University Press
Online publication date:
November 2011
Print publication year:
1996
Online ISBN:
9780511895357
DOI:
https://doi.org/10.1017/CBO9780511895357
Subjects:
Mathematics (general), Physics and Astronomy, Mathematical Methods, Probability Theory and Stochastic Processes, Statistics and Probability
Series:
Cambridge Tracts in Mathematics (119)
Information

Book description

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.

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

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