## Brazilian Journal of Probability and Statistics

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

### Gibbs measures and phase transitions on sparse random graphs

Amir Dembo and Andrea Montanari

**Full-text: Open access**

#### 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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