Percolation theory was initiated some fifty years ago as a mathematical framework for the study of random physical processes such as flow through a disordered porous medium. It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling. The aims of this book are twofold. First to present classical results in a way that is accessible to non-specialists. Second, to describe, for the first time in a book, recent results of Smirnov in conformal invariance, and outline the proof that the critical probability for random Voronoi percolation in the plane is 1/2. Throughout, the presentation is streamlined, with elegant and straightforward proofs requiring minimal background in probability and graph theory. Numerous examples illustrate the important concepts and enrich the arguments. All-in-all, it will be an essential purchase for mathematicians, physicists, electrical engineers and computer scientists working in this exciting area.
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"... A useful addition for its focus on the recent advances in two-dimensional percolation..."
Rongfeng Sun, Mathematical Reviews
Rongfeng Sun, Mathematical Reviews
Book Description
The authors' main aims are first to present classical results in a way that's accessible to non-specialists. Second, to describe, for the first time in a book, recent results of Smirnov in conformal invariance. It is essential reading for all working in this exciting area.
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4 of 4 people found the following review helpful:
5.0 out of 5 stars
Recommendable as a textbook,
By PST "A Reader from Germany" (Eislingen Deutschland) - See all my reviews
This review is from: Percolation (Hardcover)
I am what Prof. Bollobas in one of his books called a 'hobby mathematician'.
This book was my first 'contact' with percolation theory, so I cannot compare it to other books on the same subject. The book covers percolation theory mostly in the plane, only rarely does it cover d-dimensional percolation. The mathematical prerequisites are rather modest: good knowledge in probability theory, but not much of the measure theoretic part of it, is needed. Knowledge in graph theory is helpful, but not becessary. The proofs are complete and they are a little easier (more 'spelled out') than in other books by Prof. Bollabas which I have read (Modern Graph Theory, Random Graphs), but do not compormise rigor at all. I believe, this book is written not only for mathematicians. Many figures help to visualize the concepts. Except for the last 15 pages which are highly confusing, all facts and theorems needed are proven, not simply stated with a reference to some other paper. In this sense, it is a VERY good textbook. Similar to the two other books by Prof. Bollobas, also this one shows, that the author(s) know their subject matter and can motivate what's going on in a few clear words! Unlike the other two books of Prof. Bollobas this one is virtually typo-free! I think, I found about 8 harmless ones. If one is looking for a good textbook on percolation theory, I can certainly recommend this book!
5.0 out of 5 stars
Great boook, love it.,
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This review is from: Percolation (Hardcover)
Very good introduction to percolation. It is also very up to date, with chapter on recent developments.
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Inside This Book
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First Sentence:
Percolation theory was founded by Broadbent and Hammersley [1957], in order to model the flow of fluid in a porous medium with randomly blocked channels. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Harris's Lemma, Menshikov's Theorem, Smirnov's Theorem, Kesten's Theorem, Harris-Kesten Theorem, Harris's Theorem, Monte Carlo, Russo-Seymour-Welsh Theorem New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Percolation theory was founded by Broadbent and Hammersley [1957], in order to model the flow of fluid in a porous medium with randomly blocked channels. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Harris's Lemma, Menshikov's Theorem, Smirnov's Theorem, Kesten's Theorem, Harris-Kesten Theorem, Harris's Theorem, Monte Carlo, Russo-Seymour-Welsh Theorem New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 24
books:
See all 24 books this book cites
- Probability with Martingales (Cambridge Mathematical Textbooks) by David Williams in Back Matter
- Continuum Percolation (Cambridge Tracts in Mathematics) by Ronald Meester in Back Matter
- Stochastic Geometry (Wiley Series in Probability & Statistics) by Robert Harding in Back Matter
- Probability on Discrete Structures by Harry Kesten in Back Matter
- Tilings and Patterns by Branko Grunbaum in Back Matter
See all 24 books this book cites
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