Article

Probability Theory and Related Fields

, Volume 109, Issue 2, pp 183-215

First online:

Averaged and quenched propagation of chaos for spin glass dynamics

  • A. GuionnetAffiliated withMathematiques, URA 743, CNRS, Université de Paris Sud, Bâtiment 425, F-91405 Orsay, France

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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 deviations Interacting random processes Statistical mechanics Langevin dynamics
AMS Subject of Classification (1991): 60F10 60H10 60K35 82C44 82C31 82C22