Interacting particle system

Summary

An interacting particle system is a continuous-time Markov process on configurations of a lattice or graph, in which each site carries a state. The state at a site changes at rates that depend on the states of nearby sites. Each local change is simple, but infinitely many sites interact, and the system can show phase transitions. Main examples are the contact process, the voter model, the exclusion process and stochastic dynamics of the Ising model. They model epidemics, opinions, traffic and magnets.