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

Hironobu Sakagawa

doi:10.1214/EJP.v14-711

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

Hironobu Sakagawa

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 language	English
Pages (from-to)	2310-2327
Number of pages	18
Journal	Electronic Journal of Probability
Volume	14
DOIs	https://doi.org/10.1214/EJP.v14-711
Publication status	Published - 2009 Jan 1

Keywords

Gaussian field
Hard wall
Mass
Random interface
Random walk representation

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/EJP.v14-711

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

Abstract

Keywords

ASJC Scopus subject areas

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