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Probability and Phase Transition

  • Book
  • © 1994

Overview

Editors:
  1. Geoffrey Grimmett

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

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Part of the book series: Nato Science Series C: (ASIC, volume 420)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Exact Steady State Properties of the One Dimensional Asymmetric Exclusion Model

    • B. Derrida, M. R. Evans
    Pages 1-16

  3. Droplet Condensation in the Ising Model: Moderate Deviations Point of View

    • Roland L. Dobrushin, Senya B. Shlosman
    Pages 17-34

  4. Shocks in one-Dimensional Processes with Drift

    • P. A. Ferrari
    Pages 35-48

  5. Self-Organization of Random Cellular Automata: Four Snapshots

    • David Griffeath
    Pages 49-67

  6. Percolative Problems

    • Geoffrey Grimmett
    Pages 69-86

  7. Mean-Field Behaviour and the Lace Expansion

    • Takashi Hara, Gordon Slade
    Pages 87-122

  8. Long Time Tails in Physics and Mathematics

    • Frank den Hollander
    Pages 123-137

  9. Multiscale Analysis in Disordered Systems: Percolation and contact process in a Random Environment

    • Abel Klein
    Pages 139-152

  10. Geometric Representation of Lattice Models and Large Volume Asymptotics

    • Roman Kotecký
    Pages 153-176

  11. Diffusion in Random and Non-Linear PDE’s

    • A. Kupiainen
    Pages 177-189

  12. Random Walks, Harmonic Measure, and Laplacian Growth Models

    • Gregory F. Lawler
    Pages 191-208

  13. Survival and Coexistence in Interacting Particle Systems

    • T. M. Liggett
    Pages 209-226

  14. Constructive Methods in Markov Chain Theory

    • M. V. Menshikov
    Pages 227-236

  15. A Stochastic Geometric Approach to Quantum Spin Systems

    • Bruno Nachtergaele
    Pages 237-246

  16. Disordered Ising Systems and Random Cluster Representations

    • Charles M. Newman
    Pages 247-260

  17. Planar First-Passage Percolation Times are not Tight

    • R. Pemantle, Y. Peres
    Pages 261-264

  18. Theorems and Conjectures on the Droplet-Driven Relaxation of Stochastic Ising Models

    • Roberto H. Schonmann
    Pages 265-301

  19. Metastability for Markov Chains: A General Procedure Based on Renormalization Group Ideas

    • Elisabetta Scoppola
    Pages 303-322
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Keywords

About this book

This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability.
The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition.

Editors and Affiliations

  • Statistical Laboratory, University of Cambridge, Cambridge, UK

    Geoffrey Grimmett

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