Spin Glasses: A Challenge for Mathematicians

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Sprache: Englisch

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Beschreibung

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, that physicists studied by non-rigorous methods. They predicted spectacular behaviors, previously unknown in probability theory. They believe these behaviors occur in many models of considerable interest for several branches of science (statistical physics, neural networks and computer science).

This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics, and contains proofs in complete detail of much of what is rigorously known on spin glasses at the time of writing.

Über den Autor

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.

Zusammenfassung

- Written by one of the world's leading experts in the field
- Spin Glasses in the mean-field version of Sherrington and Kirkpatrick are still one of the greatest challenges in probability theory
- The author has achieved important advances in the field
- Gives a detailed and coherent presentation of recent research results in the field

Inhaltsverzeichnis

0. Introduction.- 1. A Toy Model, the REM.- 2. The Sherrington-Kirkpatrick Model.- 3. The Capacity of the Perceptron: The Ising Case.- 4. Capacity of the Perceptron: The Gaussian and the Spherical Case.- 5. The Hopfield Model.- 6. The p-Spin Interaction Model at Low Temperature.- 7. The Diluted SK Model and the K-Sat Problems.- 8. An Assignment Problem.- A. Appendix.- Elements of Probability Theory.- References.- Index.

Details

Erscheinungsjahr:	2010
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	ix 586 S.
ISBN-13:	9783642055683
ISBN-10:	3642055680
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Talagrand, Michel
Hersteller:	Springer Springer Spektrum Springer-Verlag GmbH
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 33 mm
Von/Mit:	Michel Talagrand
Erscheinungsdatum:	01.12.2010
Gewicht:	0,896 kg