Brazilian Journal of Probability and Statistics

Gibbs measures and phase transitions on sparse random graphs

Amir Dembo and Andrea Montanari

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Abstract

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.

Article information

Source
Braz. J. Probab. Stat., Volume 24, Number 2 (2010), 137-211.

Dates
First available in Project Euclid: 20 April 2010

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1271770268

Digital Object Identifier
doi:10.1214/09-BJPS027

Mathematical Reviews number (MathSciNet)
MR2643563

Zentralblatt MATH identifier
1205.05209

Keywords
Random graphs Ising model Gibbs measures phase transitions spin models local weak convergence

Citation

Dembo, Amir; Montanari, Andrea. Gibbs measures and phase transitions on sparse random graphs. Braz. J. Probab. Stat. 24 (2010), no. 2, 137--211. doi:10.1214/09-BJPS027. https://projecteuclid.org/euclid.bjps/1271770268


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