Dynamic message-passing equations for models with unidirectional dynamics

Andrey Y. Lokhov, Marc Mézard, and Lenka Zdeborová
Phys. Rev. E 91, 012811 – Published 13 January 2015

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.

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  • Received 4 July 2014

DOI:https://doi.org/10.1103/PhysRevE.91.012811

©2015 American Physical Society

Authors & Affiliations

Andrey Y. Lokhov1,*, Marc Mézard1,2, and Lenka Zdeborová3

  • 1Université Paris-Sud/CNRS, LPTMS, UMR8626, Bât. 100, 91405 Orsay, France
  • 2Ecole normale supérieure, PSL Research University, 45 rue d'Ulm, 75005 Paris, France
  • 3Institut de Physique Théorique, IPhT, CEA Saclay and CNRS URA 2306, 91191 Gif-sur-Yvette, France

  • *andrey.lokhov@lptms.u-psud.fr

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Vol. 91, Iss. 1 — January 2015

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