Anton Bovier, Pierre Picco

Mathematical Aspects of Spin Glasses and Neural Networks

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Progress in Probability 41
• Verlag: Birkhäuser / Birkhäuser Boston / Springer, Basel
• Artikelnr. des Verlages: 978-0-8176-3863-4
• 1997.
• Seitenzahl: 396
• Erscheinungstermin: 18. Dezember 1997
• Englisch
• Abmessung: 241mm x 160mm x 26mm
• Gewicht: 730g
• ISBN-13: 9780817638634
• ISBN-10: 0817638636
• Artikelnr.: 20992274

Autorenporträt

Anton Bovier is Professor of Mathematics at the University of Bonn. His research concerns applications of probability theory in physics and biology, with a focus on statistical mechanics, metastability and ageing. He has published over 130 scientific papers, and a monograph on "Statistical Mechanics of Disordered Systems". He is a Fellow of the Institute for Mathematical Statistics. He is member of the Clusters of Excellence "Hausdorff Centre for Mathematics" and "ImmunoSensation", both at the University of Bonn. Frank den Hollander is Professor of Mathematics at Leiden University. His research focuses on probability theory, statistical physics, population dynamics and complex networks. He has published over 150 scientific papers, and two monographs on "Large Deviations" and "Random Polymers". He is a member of the Royal Dutch Academy of Sciences, and a Fellow of the American Mathematical Society and of the Institute of Mathematical Statistics. He is recipient of a 5-year Advanced Grant by the European Research Council and a 10-year consortium grant by the Dutch Ministry of Education, Culture and Science.

Inhaltsangabe

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.