Overview
- 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
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (MATHE3, volume 46)
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Keywords
- Disordered Systems
- Hopfield Model
- Neural Networks
- Random Structures
- Sherrington Kirkpatrick Model
- YellowSale2006
About this book
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.
Reviews
From the reviews:
"The book presents most of the technical tools available today for a rigorous analysis of random mean field models. It will be indispensable for anyone working in the field." (Anton Bovier, Combinatorics, Probability & Computing, Issue 13, 2004)
"This book seeks to start from basics … to develop the rigorous theory, in almost complete detail. … this is a book of ideas and calculations which build upon each other to create a rich and informative theory." (David Aldous, SIAM Reviews, Vol. 47 (1), 2005)
"Each section of the book ends with some comments on the literature. … The author has … put a great effort into rendering the exposition as clear as possible. … The book will, certainly, find a favorite place on the desk of anyone working in the field." (Anton Bovier, Zentralblatt MATH, Vol. 1033 (8), 2004)
"This is a book on structures, which are very interesting for physics and – at the same time – rather fundamental for mathematics. … In conclusion, this is a very important, impressive book, written by a prominent mathematician and leading expert in the field … . the book remains indispensable as a basic introduction and reference on this extremely difficulty and interesting subject." (EMS Newsletter, March, 2006)
Bibliographic Information
Book Title: Spin Glasses: A Challenge for Mathematicians
Book Subtitle: Cavity and Mean Field Models
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Publisher: Springer Berlin, Heidelberg
Copyright Information: Springer-Verlag Berlin Heidelberg 2003
Hardcover ISBN: 978-3-540-00356-4Published: 11 July 2003
Softcover ISBN: 978-3-642-05568-3Published: 01 December 2010
Series ISSN: 0071-1136
Series E-ISSN: 2197-5655
Edition Number: 1
Number of Pages: IX, 586