Probability and Phase Transition

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

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.

• Markov chain
• Probability theory
• Renormalization group
• contact process
• interacting particle system
• random walk

• Statistical Laboratory, University of Cambridge, Cambridge, UK

  Geoffrey Grimmett

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