Confinement of the Two Dimensional Discrete Gaussian Free Field Between Two Hard Walls
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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Pages: 2310-2327
Publication Date: October 30, 2009
DOI: 10.1214/EJP.v14-711
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