Open Access
2014 On the replica symmetric solution of the $K$-sat model
Dmitry Panchenko
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Electron. J. Probab. 19: 1-17 (2014). DOI: 10.1214/EJP.v19-2963


In this paper we translate Talagrand’s solution of the $K$-sat model at high temperature into the language of asymptotic Gibbs measures. Using exact cavity equations in the infinite volume limit allows us to remove many technicalities of the inductions on the system size, which clarifies the main ideas of the proof. This approach also yields a larger region of parameters where the system is in a pure state and, in particular, for small connectivity parameter one can prove the replica symmetric formula for the free energy at any temperature.


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Dmitry Panchenko. "On the replica symmetric solution of the $K$-sat model." Electron. J. Probab. 19 1 - 17, 2014.


Accepted: 11 August 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1302.60138
MathSciNet: MR3248196
Digital Object Identifier: 10.1214/EJP.v19-2963

Primary: 60K35
Secondary: 82B44

Keywords: random K-sat model , replica symmetric solution , Spin glasses

Vol.19 • 2014
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