Sample path large deviations for Laplacian models in (1+1)-dimensions

We study scaling limits of a Laplacian pinning model in (1+1) dimension and derive sample path large deviations for the profile height function. The model is given by a Gaussian integrated random walk (or a Gaussian integrated random walk bridge) perturbed by an attractive force towards the zero-level. We study in detail the behaviour of the rate function and show that it can admit up to five minimisers depending on the choices of pinning strength and boundary conditions. This study complements corresponding large deviation results for Gaussian gradient systems with pinning in (1+1)-dimension ([FS04]) in (1+d)-dimension ([BFO09]), and recently in higher dimensions in [BCF14].