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 tree-like graphs. When applied to real-world networks, they generically provide a good analytic approximation of the real dynamics.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal-cea.archives-ouvertes.fr/cea-01140788
Contributor : Emmanuelle de Laborderie <>
Submitted on : Thursday, April 9, 2015 - 3:11:04 PM
Last modification on : Friday, March 29, 2019 - 11:28:10 AM

Links full text

Identifiers

  • HAL Id : cea-01140788, version 1
  • ARXIV : 1407.1255

Citation

Andrey Y. Lokhov, Marc Mézard, Lenka Zdeborová. Dynamic message-passing equations for models with unidirectional dynamics. 2015. ⟨cea-01140788⟩

Share

Metrics

Record views

97