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2009 Confinement of the Two Dimensional Discrete Gaussian Free Field Between Two Hard Walls
Hironobu Sakagawa
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Electron. J. Probab. 14: 2310-2327 (2009). DOI: 10.1214/EJP.v14-711

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 [S07].

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Hironobu Sakagawa. "Confinement of the Two Dimensional Discrete Gaussian Free Field Between Two Hard Walls." Electron. J. Probab. 14 2310 - 2327, 2009. https://doi.org/10.1214/EJP.v14-711

Information

Accepted: 30 October 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1196.60169
MathSciNet: MR2556019
Digital Object Identifier: 10.1214/EJP.v14-711

Subjects:
Primary: 60K35
Secondary: 82A41 , 82B24

Keywords: Gaussian field , hard wall , mass , random interface , Random walk representation

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