Confinement of the two dimensional discrete Gaussian free field between two hard walls
Hironobu Sakagawa, Department of Mathematics, Faculty of Science and Technology, Keio University
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 cite{S07}.
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