Percolation

  • Geoffrey Grimmett

Table of contents

  1. Front Matter
    Pages i-xi
  2. Geoffrey Grimmett
    Pages 1-24
  3. Geoffrey Grimmett
    Pages 25-43
  4. Geoffrey Grimmett
    Pages 44-71
  5. Geoffrey Grimmett
    Pages 72-81
  6. Geoffrey Grimmett
    Pages 82-108
  7. Geoffrey Grimmett
    Pages 109-147
  8. Geoffrey Grimmett
    Pages 148-168
  9. Geoffrey Grimmett
    Pages 169-185
  10. Geoffrey Grimmett
    Pages 186-235
  11. Geoffrey Grimmett
    Pages 236-265
  12. Back Matter
    Pages 266-296

About this book

Introduction

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.

Keywords

Mathematica cluster mathematics phase physics probability renormalization

Authors and affiliations

  • Geoffrey Grimmett
    • 1
  1. 1.School of MathematicsUniversity of BristolBristolEngland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4208-4
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-4210-7
  • Online ISBN 978-1-4757-4208-4
  • About this book