Interfacial fluctuations near the critical filling transition

We advance a method to describe the short-distance fluctuations of an interface spanning a wedge-shaped substrate near the critical filling transition. Two different length scales determined by the average distance of the interface from the substrate at the wedge center can be identified. On one length scale, the one-dimensional approximation of A. O. Parry, C. Rascon, and A. J. Wood [Phys. Rev. Lett. 85, 345 (2000)], which allows one to determine the interfacial critical exponents, is extracted from the full description. On the other scale, the short-distance fluctuations are analyzed by mean-field theory.