Information, Physics, and Computation

by Marc Mézard, Andrea Montanari

Overview

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.

Product Details

ISBN-13:	9780198570837
Publisher:	Oxford University Press
Publication date:	03/27/2009
Series:	Oxford Graduate Texts
Edition description:	New Edition
Pages:	584
Product dimensions:	7.00(w) x 9.60(h) x 4.30(d)

About the Author

Professor Marc Mezard
CNRS Research Director at Université de Paris Sud and Professor at Ecole Polytechnique, France

Marc Mezard received his PhD in 1984. He was hired in CNRS in 1981 and became research director in 1990 at Ecole Normale Supérieure. He joined the Université Paris Sud in 2001. He spent extensive periods in Rome University, in the KITP (Santa Barbara) and in MSRI (Berkeley). Author of about 150 publications, he has been awarded the silver medal of CNRS in 1990 and the Ampere price of the French academy of science in 1996. 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 Théorique de l'Ecole Normale Supérieure (LPTENS), Paris, France, and the Mathematical Sciences Research Institute, Berkeley, USA. Since 2002 he is Chargé 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.

Table of Contents

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 story

Editorial Reviews

"This book is an excellent graduate-level text on the amazing connections between modern error-correcting codes (information theory), spin glass systems (condensed matter physics), and satisfiability problems (computational complexity). Each chapter has useful exercises and a great amount of background and references for further reading on the material covered. I would expect any researcher working near the intersection of information theory, statistical physics, and combinatorial optimization to find this book to be a highly-valued resource."—James W. Harrington for Mathematical Reviews

"The authors, who are experts in these domains, open the door to important results coming out of current research in the advanced treatment of complex systems and new ways to look at important problems in computer science, mathematics, and physics."—Computing Reviews

From the Publisher