Interacting particle systems

In probability theory, an interacting particle system (IPS) is a ${\displaystyle (X(t))_{t\in \mathbb {R} ^{+}}}$ on some configuration space ${\displaystyle \Omega =S^{G}}$ given by a site space, a countable-infinite graph ${\displaystyle G}$ and a local state space, a compact metric space ${\displaystyle S}$. More precisely IPS are continuous-time Markov jump processes describing the collective behavior of stochastically interacting components. IPS are the continuous-time analogue of . Among the main examples are the voter model, the contact process, the asymmetric simple exclusion process (ASEP), the Glauber dynamics and in particular the stochastic Ising model.

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