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  • Book
  • © 1999

Percolation

Authors:

  1. Geoffrey Grimmett

    1. Statistical Laboratory, University of Cambridge, Cambridge, UK

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 321)

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  • ISBN: 978-3-662-03981-6
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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xiii
    PDF

  2. What is Percolation?

    • Geoffrey Grimmett
    Pages 1-31

  3. Some Basic Techniques

    • Geoffrey Grimmett
    Pages 32-52

  4. Critical Probabilities

    • Geoffrey Grimmett
    Pages 53-76

  5. The Number of Open Clusters per Vertex

    • Geoffrey Grimmett
    Pages 77-86

  6. Exponential Decay

    • Geoffrey Grimmett
    Pages 87-116

  7. The Subcritical Phase

    • Geoffrey Grimmett
    Pages 117-145

  8. Dynamic and Static Renormalization

    • Geoffrey Grimmett
    Pages 146-196

  9. The Supercritical Phase

    • Geoffrey Grimmett
    Pages 197-231

  10. Near the Critical Point: Scaling Theory

    • Geoffrey Grimmett
    Pages 232-253

  11. Near the Critical Point: Rigorous Results

    • Geoffrey Grimmett
    Pages 254-280

  12. Bond Percolation in Two Dimensions

    • Geoffrey Grimmett
    Pages 281-348

  13. Extensions of Percolation

    • Geoffrey Grimmett
    Pages 349-377

  14. Percolative Systems

    • Geoffrey Grimmett
    Pages 378-396

  15. Back Matter

    Pages 397-447
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About this book

Percolation theory is the study of an idealized random medium in two or more dimensions. The mathematical theory is mature, and continues to give rise to problems of special beauty and difficulty. Percolation is pivotal for studying more complex physical systems exhibiting phase transitions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. The book is intended for graduate students and researchers in probability and mathematical physics. Almost no specialist knowledge is assumed. Much new material appears in this second edition, including: dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.
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Keywords

  • Lattice
  • Mathematica
  • Percolation
  • cubic lattice
  • fields
  • mathematical physics
  • physics
  • probability
  • renormalization
  • vertices
  • combinatorics
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Authors and Affiliations

  • Statistical Laboratory, University of Cambridge, Cambridge, UK

    Geoffrey Grimmett

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Bibliographic Information

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Access via your institution
eBook USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-3-662-03981-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 149.99
Price excludes VAT (USA)
Hardcover Book USD 149.99
Price excludes VAT (USA)
Learn about institutional subscriptions