## Maximum and entropic repulsion for a Gaussian membrane model in the critical dimension

Kurt, Noemi
##### Description
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.
Comment: Published in at http://dx.doi.org/10.1214/08-AOP417 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
##### Keywords
Mathematics - Probability, 60K35, 82B41, 31B30 (Primary)