Gibbs Measures and Phase Transitions on Sparse Random Graphs
arXiv:0910.5460
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.
111 pages, 3 eps figures, Lecture notes for the 2008 Brazilian School of Probability (to appear in BJPS without Sections 1.3 and 6)
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