A closure for the master equation starting from the dynamic cavity method

We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We introduce a new such method which can be derived in a more systematic manner using the theory of Random Point Processes. Within this approach, the master equation governing the system's dynamics is closed via a set of differential equations for the auxiliary cavity probabilities. The numerical results improve on the earlier versions of the closure on several important classes of problems. We re-visit here the cases of the Ising ferromagnet and the Viana-Bray spin-glass model.