Interacting particle system

An interacting particle system is a stochastic process $(X(t))_{t\in mathbbR^{+}}$ on some cartesian product of discrete spaces $S_{g}$

$S=\times _{g\in G}S_{g}$

(where $g\in G$ with $G$ a graph. It corresponds elementary stochastic processes <math> (X_g(t))_{t \in mathbb R^+} <\math> whose time evolution takes into account the evolution of some of the others elementray stochastic processes <math> (X_{g'}(t))_{t \in mathbb R^+} <\math> according to some interaction. Usually, time is continuous and the process is a Markov one. For discrete-time it is related to Markov chains and Stochastic cellular automata.

Main examples are the voter model, the contact process.

References

• Liggett, Thomas M. (1997). "Stochastic Models of Interacting Systems". The Annals of Probability. 25 (1). Institute of Mathematical Statistics: 1–29. doi:10.2307/2959527. ISSN 0091-1798.
• Liggett, Thomas M. (1985). Interacting Particle Systems. New York: Springer Verlag. ISBN 0-387-96069-4.