Width distribution of curvature-driven interfaces: A study of universality

One-dimensional interfaces with curvature-driven growth kinetics are investigated. We calculate the steady-state distribution P(w²) of the square of the width of the interface w² and show that, as in the case for random-walk interfaces, the result can be written in a scaling form 〈w²〉P(w²)={Φ}(w²/〈w²〉), where 〈w²〉 is the average of w². The scaling function {Φ}(x) is found to be distinct from that of random-walk interfaces, but, as our Monte Carlo simulations indicate, this function is universal for curvature-driven growth. It is argued that comparison of scaling functions can be a useful method for distinguishing between universality classes of growth processes.