Confinement of the two dimensional discrete Gaussian free field between two hard walls

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Abstract

We consider the two dimensional discrete Gaussian free field confined between two hard walls. We show that the field becomes massive and identify the precise asymptotic behavior of the mass and the variance of the field as the height of the wall goes to infinity. By large fluctuation of the field, asymptotic behaviors of these quantities in the two dimensional case differ greatly from those of the higher dimensional case studied by [14].

Original languageEnglish
Pages (from-to)2310-2327
Number of pages18
JournalElectronic Journal of Probability
Volume14
Publication statusPublished - 2009

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Asymptotic Behavior
Precise Asymptotics
High-dimensional
Infinity
Fluctuations
Asymptotic behavior

Keywords

  • Gaussian field
  • Hard wall
  • Mass
  • Random interface
  • Random walk representation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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abstract = "We consider the two dimensional discrete Gaussian free field confined between two hard walls. We show that the field becomes massive and identify the precise asymptotic behavior of the mass and the variance of the field as the height of the wall goes to infinity. By large fluctuation of the field, asymptotic behaviors of these quantities in the two dimensional case differ greatly from those of the higher dimensional case studied by [14].",
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