The Martingale Method for Mean-Field Disordered Systems at High Temperature

  • Francis Comets
Part of the Progress in Probability book series (PRPR, volume 41)

Abstract

We review some martingale techniques for the study of meanfield disordered systems at high temperature, including the Sherrington-Kirkpatrick model, the Hopfield model, and more general associative memory models. We describe the log-normal limit of the partition function in term of a Brownian motion, and we give another proof of self-averaging for pressure. In the Sherrington-Kirkpatrick case we show that the law of the product of two independent configurations is close to uniform at very high temperature, but this does not persist in the whole high-temperature region.

Keywords

Entropy Filtration Nite 

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Copyright information

© Birkhäuser Boston 1998

Authors and Affiliations

  • Francis Comets
    • 1
    • 2
  1. 1.University of CaliforniaIrvineUSA
  2. 2.UFR de MathématiquesUniversité Paris 7 — Denis Diderot, URA CNRS 1321 Modèles aléatoiresParis cedex 05France

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