Dynamic scaling of the width distribution in Edwards-Wilkinson type models of interface dynamics.

Edwards-Wilkinson type models are studied in 111 dimensions and the time-dependent distribution PL(w ,t) of the square of the width of an interface w is calculated for systems of size L . We find that, using a flat interface as an initial condition, PL(w ,t) can be calculated exactly and it obeys scaling in the form ^w&`PL(w ,t)5F(w/^w&` ,t/L ), where ^w&` is the stationary value of w . For more complicated initial states, scaling is observed only in the large-time limit and the scaling function depends on the initial amplitude of the longest wavelength mode. The short-time limit is also interesting since PL(w ,t) is found to closely approximate the log-normal distribution. These results are confirmed by Monte Carlo simulations on a singlestep, solid-on-solid type model ~roof-top model! of surface evolution. @S1063-651X~96!07405-2#