Scaling of Island Distributions, Percolation, and Criticality in Contour Cuts through Wrinkled Surfaces

The statistics and critical properties of cuts through self-affine surfaces are discussed. We argue that the island distributions of such cuts are always critical. The critical exponents depend on the height of the cut and on the roughness of the interface. The correlations in such an island system are shown to be related to the system size, and the percolation transition in such a system is shown to be at a nonlocalized height.