WIDTH DISTRIBUTION FOR RANDOM-WALK INTERFACES

Roughening of a one-dimensional interface is studied under the assumption that the interface configurations are continuous, periodic random walks. The distribution of the square of the width of interface, w2, is found to scale as P(w2)=[w2]-1PHI(w2/[w2]) where [w2] is the average of w2. We calculate the scaling function PHI(x) exactly and compare it both to exact enumerations for a discrete-slope surface evolution model and to PHI's obtained in Monte Carlo simulations of equilibrium and driven interfaces of chemically reacting systems.