Mean Field Models for Spin Glasses, Volume I: Basic Examples

ISBN-13: 9783642152016 / Angielski / Twarda / 2010 / 485 str.

Michel Talagrand

Opis

This rigorous introduction to an exciting new research domain is aimed at the mathematically minded and requires no knowledge of any physics. In a new and reworked edition, this first volume presents six fundamental models and the techniques to study them.

Recenzje

From the reviews:

"It builds stone by stone a remarkable construction, revealing at each step a new piece of the fascinating picture of mean-field spin glass models. ... Enlightening explanations, written with strong commitment, help the reader to grasp the general line of thought before entering into the computations ... . With its depth and proficiency of important techniques, this book opens new perspectives on probability theory and the statistical mechanics of disordered systems. It will be a source of inspiration for generations of mathematicians." (Francis Comets, Mathematical Reviews, Issue 2012 c)

Spis treści

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.

O autorze

M. Talagrand is Research Director in CNRS, and Member of the French Academy of Sciences since 2004.