Çakmak B, Opper M. Exact solution to the random sequential dynamics of a message passing algorithm.
Phys Rev E 2021;
103:L030101. [PMID:
33862681 DOI:
10.1103/physreve.103.l030101]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Accepted: 02/10/2021] [Indexed: 11/07/2022]
Abstract
We analyze the random sequential dynamics of a message passing algorithm for Ising models with random interactions in the large system limit. We derive exact results for the two-time correlation functions and the speed of convergence. The de Almedia-Thouless stability criterion of the static problem is found to be necessary and sufficient for the global convergence of the random sequential dynamics.
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