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July 2010 Gibbs measures and phase transitions on sparse random graphs
Amir Dembo, Andrea Montanari
Braz. J. Probab. Stat. 24(2): 137-211 (July 2010). DOI: 10.1214/09-BJPS027


Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sparse graph. In recent years, considerable progress has been achieved by viewing these distributions as Gibbs measures and applying to their study heuristic tools from statistical physics. We review this approach and provide some results towards a rigorous treatment of these problems.


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Amir Dembo. Andrea Montanari. "Gibbs measures and phase transitions on sparse random graphs." Braz. J. Probab. Stat. 24 (2) 137 - 211, July 2010.


Published: July 2010
First available in Project Euclid: 20 April 2010

zbMATH: 1205.05209
MathSciNet: MR2643563
Digital Object Identifier: 10.1214/09-BJPS027

Keywords: Gibbs measures , Ising model , Local weak convergence , Phase transitions , Random graphs , spin models

Rights: Copyright © 2010 Brazilian Statistical Association


Vol.24 • No. 2 • July 2010
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