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Percolation

  • Textbook
  • © 1989

Overview

Authors:
  1. Geoffrey Grimmett

    1. School of Mathematics, University of Bristol, Bristol, England

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xi
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  2. What Is Percolation?

    • Geoffrey Grimmett
    Pages 1-24

  3. Some Basic Techniques

    • Geoffrey Grimmett
    Pages 25-43

  4. The Uniqueness of the Critical Point

    • Geoffrey Grimmett
    Pages 44-71

  5. The Number of Open Clusters per Vertex

    • Geoffrey Grimmett
    Pages 72-81

  6. The Subcritical Phase

    • Geoffrey Grimmett
    Pages 82-108

  7. The Supercritical Phase

    • Geoffrey Grimmett
    Pages 109-147

  8. Near the Critical Point: Scaling Theory

    • Geoffrey Grimmett
    Pages 148-168

  9. Near the Critical Point: Rigorous Results

    • Geoffrey Grimmett
    Pages 169-185

  10. Bond Percolation in Two Dimensions

    • Geoffrey Grimmett
    Pages 186-235

  11. A Miscellany of Random Processes

    • Geoffrey Grimmett
    Pages 236-265

  12. Back Matter

    Pages 266-296
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Keywords

About this book

Quite apart from the fact that percolation theory had its ongm in an honest applied problem, it is a source of fascinating problems of the best kind for which a mathematician can wish: problems which are easy to state with a minimum of preparation, but whose solutions are apparently difficult and require new methods. At the same time, many of the prob­ lems are of interest to or proposed by statistical physicists and not dreamed up merely to demonstrate ingenuity. Much progress has been made in recent years, and many of the open problems of ten years aga have been solved. With such solutions we have seen the evolution of new techniques and questions; the consequent knowledge has shifted the ground under percolation, and it is time to examine afresh the mathematics of the subject. The quantity of literature related to percolation seems to grow hour by hour, mostly in the physics journals. It is becoming increasingly diffi­ cult to get to know the subject from scratch, and one of the principal purposes of this book is to remedy this. This book is about the mathematics of percolation theory, with the emphasis upon presenting the shortest rigorous proofs of the main facts.

Authors and Affiliations

  • School of Mathematics, University of Bristol, Bristol, England

    Geoffrey Grimmett

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