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(${\mathit{w}}^2$) of the square of the width of the interface ${\mathit{w}}^2$ and show that, as in the case for random-walk interfaces, the result can be written in a scaling form 〈${\mathit{w}}^2$〉P(${\mathit{w}}^2$)=Φ(${\mathit{w}}^2$/〈${\mathit{w}}^2$〉), where 〈${\mathit{w}}^2$〉 is the average of ${\mathit{w}}^2$. 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.