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.
"Gibbs measures and phase transitions on sparse random graphs." Braz. J. Probab. Stat. 24 (2) 137 - 211, July 2010. https://doi.org/10.1214/09-BJPS027