Interacting particle system
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An interacting particle system is a stochastic process :Failed to parse (unknown function "\math"): {\displaystyle (X(t))_{t \in mathbb R^+} <\math> on some cartesian product of discrete spaces <math> S_g <\math> :<math> S= \times_{g \in G} S_g } (where <math> g \in G <\math> with <math> G <\math> 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.