Large deviations for Langevin spin glass dynamics

G. B. Arous, A. Guionnet

Research output: Contribution to journalArticle

Abstract

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 measure Q 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 to Q in the case of a symmetric initial law and even potential for the free spin.

Original languageEnglish (US)
Pages (from-to)455-509
Number of pages55
JournalProbability Theory and Related Fields
Volume102
Issue number4
DOIs
StatePublished - Dec 1995

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Spin Glass
Large Deviations
Empirical Measures
Large Deviation Principle
Path Space
Rate Function
Probability Measure
Deduce
Asymptotic Behavior
Converge
Model

Keywords

  • Mathematics Subject Classification: 60F10, 60H10, 60K35, 82C44

ASJC Scopus subject areas

  • Statistics and Probability
  • Analysis
  • Mathematics(all)

Cite this

Large deviations for Langevin spin glass dynamics. / Arous, G. B.; Guionnet, A.

In: Probability Theory and Related Fields, Vol. 102, No. 4, 12.1995, p. 455-509.

Research output: Contribution to journalArticle

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