Probability Theory and Related Fields

, Volume 102, Issue 4, pp 455–509

Large deviations for Langevin spin glass dynamics

  • G. B. Arous
  • A. Guionnet

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 δQ. 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

Authors and Affiliations

  • G. B. Arous
    • 1
  • A. Guionnet
    • 2
  1. 1.URA 762, CNRS, DMIEcole Normale SuperieureParisFrance
  2. 2.URA 743, CNRSUniversité de Paris SudOrsayFrance

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