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Large deviations for Langevin spin glass dynamics
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  • Published: December 1995

Large deviations for Langevin spin glass dynamics

  • G. B. Arous1 &
  • A. Guionnet2 

Probability Theory and Related Fields volume 102, pages 455–509 (1995)Cite this article

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Summary

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.

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Author information

Authors and Affiliations

  1. URA 762, CNRS, DMI, Ecole Normale Superieure, F-75230, Paris, France

    G. B. Arous

  2. URA 743, CNRS, Université de Paris Sud, Bat. 425, F-91405, Orsay, France

    A. Guionnet

Authors
  1. G. B. Arous
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  2. A. Guionnet
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Arous, G.B., Guionnet, A. Large deviations for Langevin spin glass dynamics. Probab. Th. Rel. Fields 102, 455–509 (1995). https://doi.org/10.1007/BF01198846

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  • Received: 27 January 1994

  • Revised: 01 February 1995

  • Issue Date: December 1995

  • DOI: https://doi.org/10.1007/BF01198846

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Mathematics Subject Classification

  • 60F10
  • 60H10
  • 60K35
  • 82C44
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