Probability Theory and Related Fields

, Volume 109, Issue 2, pp 183–215

Averaged and quenched propagation of chaos for spin glass dynamics

Authors

  • A. Guionnet
    • Mathematiques, URA 743, CNRS, Université de Paris Sud, Bâtiment 425, F-91405 Orsay, France
Article

DOI: 10.1007/s004400050130

Cite this article as:
Guionnet, A. Probab Theory Relat Fields (1997) 109: 183. doi:10.1007/s004400050130
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Summary.

We study the asymptotic behaviour for both asymmetric and symmetric spin glass dynamics in a Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We prove, without any condition on time and temperature, averaged propagation of chaos results. Extending this result to replicated systems, we conclude that the law of a single spin converges to a non Markovian probability measure, in law with respect to the random interaction.

Key words:Large deviationsInteracting random processesStatistical mechanicsLangevin dynamics
AMS Subject of Classification (1991): 60F1060H1060K3582C4482C3182C22

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© Springer-Verlag Berlin Heidelberg 1997