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We compare dynamic mean-field and dynamic cavity as methods to describe thestationary states of dilute kinetic Ising models. We compute dynamic mean-fieldtheory by expanding in interaction strength to third order, and compare to theexact dynamic mean-field theory for fully asymmetric networks. We show that indiluted networks the dynamic cavity method generally predicts magnetizations ofindividual spins better than both first order ("naive") and second order("TAP") dynamic mean field theory.

Dynamic mean-field and cavity methods for diluted Ising systems