Probability Theory and Related Fields

, Volume 102, Issue 4, pp 455–509

Large deviations for Langevin spin glass dynamics


  • G. B. Arous
    • URA 762, CNRS, DMIEcole Normale Superieure
  • A. Guionnet
    • URA 743, CNRSUniversité de Paris Sud

DOI: 10.1007/BF01198846

Cite this article as:
Arous, G.B. & Guionnet, A. Probab. Th. Rel. Fields (1995) 102: 455. doi:10.1007/BF01198846


We study the asymptotic behaviour of asymmetrical spin glass dynamics in a Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We prove that the annealed law of the empirical measure on path space of these dynamics satisfy a large deviation principle in the high temperature regime. We study the rate function of this large deviation principle and prove that it achieves its minimum value at a unique probability measureQ which is not markovian. We deduce that the quenched law of the empirical measure converges to δ Q . Extending then the preceeding results to replicated dynamics, we investigate the quenched behavior of a single spin. We get quenched convergence toQ in the case of a symmetric initial law and even potential for the free spin.

Mathematics Subject Classification

60F10 60H10 60K35 82C44

Copyright information

© Springer-Verlag 1995