16. Interacting Particle Systems

Summary

An interacting particle system consists of a collection of particles. Each particle has a state, selected from a finite set of possible states. The system evolves with time, with the state of each particle dependent in a probabilistic way on the states of its neighbors.

Topics

1. The Fire Process
2. The Voter Process

Applets

• The Fire Experiment
• The Voter Experiment

Topics in PDF Format

• The Fire Process
• The Voter Process

External Resources

• Percolation, by Geoffrey Grimmett is a good introduction to percolation.
• Lecture Notes on Particle Systems and Percolation, by Richard Durrett is a concise, higher level introduction.
• Interacting Particle Systems, by Thomas Liggett is perhaps the definitive treatment of particle systems.
• Young Men and Fire by Norman Maclean is a compelling study of a real fire.
• Primordial Soup Kitchen is the definitive site for interacting particle systems and cellular automata.