Laplacian interface models: the Gaussian case in high dimensions

Random interface models have been an important object of study during the last decades. Next to the widely studied gradient model, the Laplacian model is of importance in modelling for example semiflexible membranes. In this talk, we present the Gaussian Laplacian model, that is, the Gausian field on the d-dimensional integer lattice with covariances given by the Green's function of the discrete bilaplacian. We compare it with the gradient model, and explain why crucial techniques like the random walk representation and the FKG inequalities fail. We show the methods we use to avoid some of these problems, and prove entropic repulsion for the Laplacian model in sufficiently high dimensions.