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

Gérard Ben Arous, Michel Sortais

Research output: Contribution to journalArticlepeer-review

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

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability

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