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Percolation

Percolation

$99.99 (P)

  • Date Published: September 2006
  • availability: Available
  • format: Hardback
  • isbn: 9780521872324

$ 99.99 (P)
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About the Authors
  • 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, first published in 2006, are twofold. First to present classical results in a way that is accessible to non-specialists. Second, to describe 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.

    • Systematically presents probabilistic and graph theory tools for percolation, and that describes Smirnov's results in conformal invariance
    • Streamlined presentation requiring only minimal background in probability and graph theory
    • Numerous examples illustrate the important concepts and enrich the arguments
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    Reviews & endorsements

    "... A useful addition for its focus on the recent advances in two-dimensional percolation..."
    Rongfeng Sun, Mathematical Reviews

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    Product details

    • Date Published: September 2006
    • format: Hardback
    • isbn: 9780521872324
    • length: 334 pages
    • dimensions: 235 x 161 x 20 mm
    • weight: 0.66kg
    • contains: 112 b/w illus.
    • availability: Available
  • Table of Contents

    Preface
    1. Basic concepts
    2. Probabilistic tools
    3. Percolation on Z2 - the Harris-Kesten theorem
    4. Exponential decay and critical probabilities - theorems of Menshikov and Aizenman & Barsky
    5. Uniqueness of the infinite open cluster and critical probabilities
    6. Estimating critical probabilities
    7. Conformal invariance - Smirnov's theorem
    8. Continuum percolation
    Bibliography
    Index
    List of notation.

  • Authors

    Bela Bollobás, Trinity College, Cambridge
    Béla Bollobás is a Senior Research Fellow at Trinity College, Cambridge and is the Jabie Hardin Chair of Excellence in Combinatorics at the University of Memphis. He has held visiting positions from Seattle to Singapore, from Brazil to Zurich. This is his eleventh book.

    Oliver Riordan, Trinity College, Cambridge
    Oliver Riordan is a Royal Society Research Fellow in the University of Cambridge and Research Fellow of Trinity College, Cambridge. In May 2000 he shared the prize for solving Christopher Monckton's Eternity Puzzle.

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