This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. It is accessible to graduate students and researchers without a specific training in any of these fields. The selected topics include spin glasses, error correcting codes, satisfiability, and are central to each field. The approach focuses on large random instances and adopts a common probabilistic formulation in terms of graphical models. It presents message passing algorithms like belief propagation and survey propagation, and their use in decoding and constraint satisfaction solving. It also explains analysis techniques like density evolution and the cavity method, and uses them to study phase transitions.
Dr Andrea Montanari Assistant Professor, Stanford University and CNRS France Andrea Montanari received a Laurea degree in Physics in 1997, and a Ph. D. in Theoretical Physics in 2001 (both from Scuola Normale Superiore in Pisa, Italy). He has been post-doctoral fellow at Laboratoire de Physique Theorique de l'Ecole Normale Superieure (LPTENS), Paris, France, and the Mathematical Sciences Research Institute, Berkeley, USA. Since 2002 he is Charge de Recherche (a permanent research position with Centre National de la Recherche Scientifique, CNRS) at LPTENS. In September 2006 he joined Stanford University as Assistant Professor in the Departments of Electrical Engineering and Statistics. In 2006 he was awarded the CNRS bronze medal for theoretical physics.
1. Introduction to Information Theory ; 2. Statistical physics and probability theory ; 3. Introduction to combinatorial optimization ; 4. Probabilistic toolbox ; 5. The Random Energy Model ; 6. Random Code Ensemble ; 7. Number partitioning ; 8. Introduction to replica theory ; 9. Factor graphs and graph ensembles ; 10. Satisfiability ; 11. Low-Density Parity-Check Codes ; 12. Spin glasses ; 13. Bridges: Inference and Monte Carlo ; 14. Belief propagation ; 15. Decoding with belief propagation ; 16. The assignment problem ; 17. Ising models on random graphs ; 18. Linear Boolean equations ; 19. The 1RSB cavity method ; 20. Random K-satisfiability ; 21. Glassy states in coding theory ; 22. An ongoing story
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- ID: 9780198570837
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