In probability theory, an interacting particle system is a stochastic process t ∈ R + {\displaystyle _{t\in \mathbb {R} ^{+}}} on some configuration space Ω = S G {\displaystyle \Omega =S^{G}} given by a site space, a countable-infinite graph G {\displaystyle G} and a local state space, a compact metric space S {\displaystyle S}. Wikipedia