Information, Physics, and Computation [Hardcover]

A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.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, adopting 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.1. Introduction to Information Theory2. Statistical physics and probability theory3. Introduction to combinatorial optimization4. Probabilistic toolbox5. The Random Energy Model6. Random Code Ensemble7. Number partitioning8. Introduction to replica theory9. Factor graphs and graph ensembles10. Satisfiability11. Low-Density Parity-Check Codes12. Spin glasses13. Bridges: Inference and Monte Carlo14. Belief propagation15. Decoding with belief propagation16. The assignment problem17. Ising models on random graphs18. Linear Boolean equations19. The 1RSB cavity method20. Random K-satisfiability21. Glassy states in coding theory22. An ongoing storyProfessor Marc MezardCNRS Research Director at Universit? de Paris Sud and Professor at Ecole Polytechnique, FranceMarc Mezard received his PhD in 1984. He was hired in CNRS in 1981 and became research director in 1990 at Ecole Normall³