title: Dynamic message-passing equations for models with unidirectional dynamics.
abstract: Understanding and quantifying the dynamics of disordered out-of-equilibrium models is an important problem in many branches of science. Using the dynamic cavity method on time trajectories, we construct a general procedure for deriving the dynamic message-passing equations for a large class of models with unidirectional dynamics, which includes the zero-temperature random-field Ising model, the susceptible-infected-recovered model, and rumor spreading models. We show that unidirectionality of the dynamics is the key ingredient that makes the problem solvable. These equations are applicable to single instances of the corresponding problems with arbitrary initial conditions and are asymptotically exact for problems defined on locally treelike graphs. When applied to real-world networks, they generically provide a good analytic approximation of the real dynamics.
authors: Université Paris-Sud/CNRS, LPTMS, UMR8626, Bât. 100, 91405 Orsay, France.
authors: Andrey Y
authors: AY
authors: Lokhov
authors: Université Paris-Sud/CNRS, LPTMS, UMR8626, Bât. 100, 91405 Orsay, France and Ecole normale supérieure, PSL Research University, 45 rue d'Ulm, 75005 Paris, France.
authors: Marc
authors: M
authors: Mézard
authors: Institut de Physique Théorique, IPhT, CEA Saclay and CNRS URA 2306, 91191 Gif-sur-Yvette, France.
authors: Lenka
authors: L
authors: Zdeborová