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Percolation Theory and Ergodic Theory of Infinite Particle Systems

  • Book
  • © 1987

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Editors:
  1. Harry Kesten

    1. Institute for Mathematics and Its Applications, Minneapolis, USA

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Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 8)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Rapid Convergence to Equilibrium of Stochastic Ising Models in the Dobrushin Shlosman Regime

    • M. Aizenman, R. Holley
    Pages 1-11

  3. Uniqueness of the Infinite Cluster and Related Results in Percolation

    • M. Aizenman, H. Kesten, C. M. Newman
    Pages 13-20

  4. Survival of Cyclical Particle Systems

    • Maury Bramson, David Griffeath
    Pages 21-29

  5. Expansions in Statistical Mechanics as Part of the Theory of Partial Differential Equations

    • D. C. Brydges
    Pages 31-47

  6. The Mean Field Bound for the Order Parameter of Bernoulli Percolation

    • J. T. Chayes, L. Chayes
    Pages 49-71

  7. Recent Results for the Stepping Stone Model

    • J. Theodore Cox, David Griffeath
    Pages 73-83

  8. Stochastic Growth Models

    • R. Durrett, R. H. Schonmann
    Pages 85-119

  9. Random Walks and Diffusions on Fractals

    • Sheldon Goldstein
    Pages 121-129

  10. The Behavior of Processes with Statistical Mechanical Properties

    • Lawrence Gray
    Pages 131-167

  11. Stiff Chains and Levy Flight: Two Self Avoiding Walk Models and the Uses of Their Statistical Mechanical Representations

    • J. W. Halley
    Pages 169-185

  12. One Dimensional Stochastic Ising Models

    • Richard Holley
    Pages 187-202

  13. A Scaling relation at criticality for 2D-Percolation

    • Harry Kesten
    Pages 203-212

  14. Reversible Growth Models on Zd: Some Examples

    • Thomas M. Liggett
    Pages 213-227

  15. Inequalities for γ and Related Critical Exponents in Short and Long Range Percolation

    • C. M. Newman
    Pages 229-244

  16. A New Look at Contact Processes in Several Dimensions

    • Roberto H. Schonmann
    Pages 245-250

  17. Fractal and Multifractal Approaches to Percolation: Some Exact and Not-So-Exact Results

    • H. Eugene Stanley
    Pages 251-299

  18. Surface Simulations for Large Eden Clusters

    • D. Stauffer
    Pages 301-309

  19. Duality for k-Degree Percolation on the Square Lattice

    • John C. Wierman
    Pages 311-323
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Keywords

About this book

This IMA Volume in ~athematics and its Applications PERCOLATION THEORY AND ERGODIC THEORY OF INFINITE PARTICLE SYSTEMS represents the proceedings of a workshop which was an integral part of the 19R4-85 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS We are grateful to the Scientific Committee: naniel Stroock (Chairman) Wendell Fleming Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaoo for planning and implementing an exciting and stimulating year-long program. We especially thank the Workshop Organizing Committee, Harry Kesten (Chairman), Richard Holley, and Thomas Liggett for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinherger PREFACE Percolation theory and interacting particle systems both have seen an explosive growth in the last decade. These suhfields of probability theory are closely related to statistical mechanics and many of the publications on these suhjects (especially on the former) appear in physics journals, wit~ a great variahility in the level of rigour. There is a certain similarity and overlap hetween the methods used in these two areas and, not surprisingly, they tend to attract the same probabilists. It seemed a good idea to organize a workshop on "Percolation Theory and Ergodic Theory of Infinite Particle Systems" in the framework of the special probahility year at the Institute for Mathematics and its Applications in 1985-86. Such a workshop, dealing largely with rigorous results, was indeed held in February 1986.

Editors and Affiliations

  • Institute for Mathematics and Its Applications, Minneapolis, USA

    Harry Kesten

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