Large deviations in the Langevin dynamics of a short-range spin glass

Gérard Ben Arous, Michel Sortais

Research output: Contribution to journalArticle

Abstract

We consider a Langevin dynamics associated with a d-dimensional Edwards-Anderson model having Gaussian coupling variables, and show that the averaged law of the empirical process satisfies a large-deviation principle according to a good rate functional Ia having a unique minimizer Qx. The asymptotic dynamics Q may be characterized as the unique weak solution corresponding to a non-Markovian system of interacting diffusions having an infinite range of interaction. We then establish that the quenched law of the empirical process also obeys a large-deviation process, according to a (deterministic) good rate functional Iq satisfying Iq ≥ Ia, so that, for a typical realization of the disorder variables, the quenched law of the empirical process also converges exponentially fast to a Dirac mass concentrated at Q.

Original languageEnglish (US)
Pages (from-to)921-954
Number of pages34
JournalBernoulli
Volume9
Issue number6
DOIs
StatePublished - Dec 2003

Fingerprint

Langevin Dynamics
Empirical Process
Spin Glass
Large Deviations
Interacting Diffusions
Range of data
Anderson Model
Large Deviation Principle
Minimizer
Paul Adrien Maurice Dirac
Weak Solution
Disorder
Converge
Interaction

Keywords

  • Disordered systems
  • Interacting diffusion processes
  • Large deviations
  • Statistical mechanics

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Large deviations in the Langevin dynamics of a short-range spin glass. / Ben Arous, Gérard; Sortais, Michel.

In: Bernoulli, Vol. 9, No. 6, 12.2003, p. 921-954.

Research output: Contribution to journalArticle

Ben Arous, Gérard ; Sortais, Michel. / Large deviations in the Langevin dynamics of a short-range spin glass. In: Bernoulli. 2003 ; Vol. 9, No. 6. pp. 921-954.
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