Symmetric langevin spin glass dynamics

G. Ben Arous, A. Guionnet

Research output: Contribution to journalArticle

Abstract

We study the asymptotic behavior of symmetric spin glass dynamics in the Sherrington-Kirkpatrick model as proposed by Sompolinsky-Zippelius. We prove that the averaged law of the empirical measure on the path space of these dynamics satisfies a large deviation upper bound in the high temperature regime. We study the rate function which governs this large deviation upper bound and prove that it achieves its minimum value at a unique probability measure Q which is not Markovian. We deduce an averaged and a quenched law of large numbers. We then study the evolution of the Gibbs measure of a spin glass under Sompolinsky-Zippelius dynamics. We also prove a large deviation upper bound for the law of the empirical measure and describe the asymptotic behavior of a spin on path space under this dynamic in the high temperature regime.

Original languageEnglish (US)
Pages (from-to)1367-1422
Number of pages56
JournalAnnals of Probability
Volume25
Issue number3
StatePublished - Jul 1997

Fingerprint

Spin Glass
Large Deviations
Path Space
Empirical Measures
Upper bound
Asymptotic Behavior
Gibbs Measure
Rate Function
Law of large numbers
Probability Measure
Deduce
Large deviations
Asymptotic behavior
Model

Keywords

  • Interacting random processes
  • Langevin dynamics
  • Large deviations
  • Statistical mechanics

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Symmetric langevin spin glass dynamics. / Ben Arous, G.; Guionnet, A.

In: Annals of Probability, Vol. 25, No. 3, 07.1997, p. 1367-1422.

Research output: Contribution to journalArticle

Ben Arous, G & Guionnet, A 1997, 'Symmetric langevin spin glass dynamics', Annals of Probability, vol. 25, no. 3, pp. 1367-1422.
Ben Arous, G. ; Guionnet, A. / Symmetric langevin spin glass dynamics. In: Annals of Probability. 1997 ; Vol. 25, No. 3. pp. 1367-1422.
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