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