  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.
