October 2022 Belief propagation on the random k-SAT model
Amin Coja-Oghlan, Noela Müller, Jean B. Ravelomanana
Author Affiliations +
Ann. Appl. Probab. 32(5): 3718-3796 (October 2022). DOI: 10.1214/21-AAP1772


Corroborating a prediction from statistical physics, we prove that the belief propagation message passing algorithm approximates the partition function of the random k-SAT model well for all clause/variable densities and all inverse temperatures for which a modest absence of long-range correlations condition is satisfied. This condition is known as “replica symmetry” in physics language. From this result we deduce that a replica symmetry breaking phase transition occurs in the random k-SAT model at low temperature for clause/variable densities below but close to the satisfiability threshold.

Funding Statement

The first author was supported by DFG CO 646/3 and DFG CO 646/4.
The second author was supported in part by ERC-Grant 772606-PTRCSP.
The third author was supported by DFG CO 646/4.


The authors would like to thank the anonymous referees and the Editor for their constructive comments that improved the quality of this paper.


Download Citation

Amin Coja-Oghlan. Noela Müller. Jean B. Ravelomanana. "Belief propagation on the random k-SAT model." Ann. Appl. Probab. 32 (5) 3718 - 3796, October 2022. https://doi.org/10.1214/21-AAP1772


Received: 1 November 2020; Revised: 1 October 2021; Published: October 2022
First available in Project Euclid: 18 October 2022

MathSciNet: MR4497857
zbMATH: 1498.60044
Digital Object Identifier: 10.1214/21-AAP1772

Primary: 60C05 , 68Q87

Keywords: belief propagation , k-SAT , phase transition , replica symmetry breaking

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.32 • No. 5 • October 2022
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