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基本説明
Sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.
Full Description
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.
Contents
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
