Critical behavior of the massless free field at the depinning transition

We consider the d-dimensional massless free field localized by a delta -pin ning of strength epsilon. We study the asymptotics of the variance of the f ield (when d = 2), and of the decay-rate of its 2-point function (when d gr eater than or equal to 2), as epsilon goes to zero, for general Gaussian in teractions. Physically speaking, we thus rigorously obtain the critical beh avior of the transverse and longitudinal correlation lengths of the corresp onding d + 1-dimensional effective interface model in a non-mean-field regi me. We also describe the set of pinned sites at small epsilon, for a broad class of d-dimensional massless models.