Information, Physics, and Computation

Erscheinungsjahr 2014
ISBN: 978-0-19-857083-7
Verlag: ACADEMIC

Buch, Englisch, 584 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 1279 g

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.

Zielgruppe

Graduate students, researchers, and lecturers in statistical physics, information theory, and theoretical computer science.

Autoren/Hrsg.

Mézard, Marc

Montanari, Andrea

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Inhaltsverzeichnis

- 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

Über Autor(innen)

Mézard, Marc
Marc Mézard, Laboratoire de Physique Théorique et Modeles Statistiques, Université de Paris Sud, Orsay, France

Montanari, Andrea
Andrea Montanari, Electrical Engineering and Statistics Department, Stanford University, USA

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.