Grimmett G. (ed.) Probability and Phase Transition

Amsterdam: Springer, 1994. — 334 p.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.Exact Steady State Properties of the One Dimensional Asymmetric Exclusion Model
Droplet Condensation in the Ising Model: Moderate Deviations Point of View
Shocks in one-Dimensional Processes with Drift
Self-Organization of Random Cellular Automata: Four Snapshots
Percolative Problems
Mean-Field Behaviour and the Lace Expansion
Long Time Tails in Physics and Mathematics
Multiscale Analysis in Disordered Systems: Percolation and contact process in a Random Environment
Geometric Representation of Lattice Models and Large Volume Asymptotics
Diffusion in Random and Non-Linear PDE’s
Random Walks, Harmonic Measure, and Laplacian Growth Models
Survival and Coexistence in Interacting Particle Systems
Constructive Methods in Markov Chain Theory
A Stochastic Geometric Approach to Quantum Spin Systems
Disordered Ising Systems and Random Cluster Representations
Planar First-Passage Percolation Times are not Tight
Theorems and Conjectures on the Droplet-Driven Relaxation of Stochastic Ising Models
Metastability for Markov Chains: A General Procedure Based on Renormalization Group Ideas