Large deviations for the Ginzburg-Landau ∇ φ interface model

T. Funaki, T. Nishikawa

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Hydrodynamic large scale limit for the Ginzburg-Landau ∇φ interface model was established in [6]. As its next stage this paper studies the corresponding large deviation problem. The dynamic rate functional is given by I (h) = 1/4 (latin small letter esh)T0 dt (latin small letter esh)double struck T sign d {∂h/∂t - div (∇σ (Vh))}2 dθ for h = h(t, θ), t ∈ [0, T], θ ∈ double struck Td, where σ = σ (u) is the surface tension for mean tilt u ∈ double struck Rd. Our main tool is H-1-method exploited by Landim and Yau [9]. The relationship to the rate functional obtained under the static situation by Deuschel et al. [3] is also discussed.

Original languageEnglish
Pages (from-to)535-568
Number of pages34
JournalProbability Theory and Related Fields
Volume120
Issue number4
DOIs
Publication statusPublished - 2001 Aug
Externally publishedYes

Keywords

  • Effective interfaces
  • Ginzburg-Landau model
  • Hydrodynamic limit
  • Large deviations
  • Massless fields

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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