Localization of a Gaussian membrane model with weak pinning potentials

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Abstract

We consider a class of effective models on ℤd called Gaussian membrane models with square-well pinning or σ-pinning. It is known that when d = 1 this model exhibits a localization/delocalization transition that depends on the strength of the pinning. In this paper, we show that when d ≥ 2, once we impose weak pinning potentials the field is always localized in the sense that the corresponding free energy is always positive. We also discuss the case that both square-well potentials and repulsive potentials are acting in high dimensions.

Original languageEnglish
Pages (from-to)1123-1140
Number of pages18
JournalAlea
Volume15
Issue number2
DOIs
Publication statusPublished - 2018 Jan 1

Keywords

  • Free energy
  • Localization
  • Pinning
  • Random membrane

ASJC Scopus subject areas

  • Statistics and Probability

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