This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians". This new edition will appear in two volumes, the present first volume presents the basic results and methods, the second volume is expected to appear in 2011. In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The first volume of this new and completely rewritten edition presents six fundamental models and the basic techniques to study them.

Completely rewritten, updated and enlarged edition of Talagrand's Ergebnisse Vol. 46: "Spin Glasses: A Challenge for Mathematicians" (2003) in two volumes. Will bring a reader with no previous knowledge of Spin Glasses to the frontier of current research. The only fully rigorous treatise of this scale on the subject. This first volume presents the basic results and methods. Includes supplementary material: sn.pub/extras

Autorentext

Michel Talagrand has made profound contributions to mathematics, notably in probability theory and related topics. The author of several books and well over 200 research papers, he is the recipient of several awards, including the Loève Prize, the Fermat Prize and the Shaw Prize. He has been a plenary speaker at the International Congress of Mathematicians and is a member of the French Academy of Sciences.

Inhalt
Introduction.- 1. The Sherrington-Kirkpatrick Model.- 2. The Perceptron Model.- 3. The Shcherbina and Tirozzi Model.- 4. The Hopfield Model.- 5. The V-statistics Model.- 6. The Diluted SK Model and the K-Sat Problem.- 7. An Assignment Problem.- A. Appendix: Elements of Probability Theory.- References.- Index.- Glossary.