Mean field models for spin glasses, Volume I, basic examples / Michel Talagrand

Contient des exercices

Bibliogr. p. 465-473. Glossaire. Index

The book consists of 7 chapters. In Chapter 1, the Sherington-Kirkpatrick model (SK) is studied, which is the “original” spin glass, at sufficiently high temperature. This model serves as an introduction to the basic ideas and methods. In Chapters 2 and 3, the “perceptron capacity model” is considered. This model is fundamental in the theory of neural networks. The Hopfield model is considered in Chapter 4 using an approach invented by A. Bovier and V. Gayzard. Chapter 5 introduces a new model based on V-statistics. It is connected to the perceptron model of Chapter 2, but with a remarkable twist. The last two chapters present models that are different from the previous ones: Chapter 6 studies a common generalization of the diluted SK model, while Chapter 7 is motivated by the random assignment problem. The book also contains an appendix which recalls many basic facts of probability theory.