%0 Journal Article
%T Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension
%A Noemi Kurt
%J Mathematics
%D 2008
%I arXiv
%R 10.1214/08-AOP417
%X We consider the real-valued centered Gaussian field on the four-dimensional integer lattice, whose covariance matrix is given by the Green's function of the discrete Bilaplacian. This is interpreted as a model for a semiflexible membrane. $d=4$ is the critical dimension for this model. We discuss the effect of a hard wall on the membrane, via a multiscale analysis of the maximum of the field. We use analytic and probabilistic tools to describe the correlation structure of the field.
%U http://arxiv.org/abs/0801.0551v3