Mathematical Aspects of Spin Glasses and Neural Networks

Aimed at graduates and potential researchers, this is a comprehensive introduction to the mathematical aspects of spin glasses and neural networks. It should be useful to mathematicians in probability theory and theoretical physics, and to engineers working in theoretical computer science.

1: Statics. - 1. 1 Mean Field Models. - Hopfield Models as Generalized Random Mean Field Models. - The Martingale Method for Mean-Field Disordered Systems at High Temperature. - On the Central Limit Theorem for the Overlap in the Hopfield Model. - Limiting Behavior of Random Gibbs Measures: Metastates in Some Disordered Mean Field Models. - On the Storage Capacity of the Hopfield Model. - 1. 2 Lattice Models. - Typical Profiles of the Kac-Hopfield Model. - Thermodynamic Chaos and the Structure of Short-Range Spin Glasses. - Random Spin Systems with Long-Range Interactions. - 2: Dynamics. - Langevin Dynamics for Sherrington-Kirkpatrick Spin Glasses. - Sherrington-Kirkpatrick Spin-Glass Dynamics Part II: The Discrete Setting.