Abstract
AbstractThe scope of these lecture notes is to provide an introduction to modern statistical physics mean-field methods for the study of phase transitions and optimization problems over random structures. We first give a brief introduction to the field using as tutorial example the percolation problem in random graphs. Next we describe the so called cavity method and the related message-passing algorithms (Belief Propagation and variants) which can be used to analyze and solve optimization problems over random structures.KeywordsPartition FunctionRandom GraphConstraint Satisfaction ProblemSoft ConstraintHard ConstraintThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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