We study an anomalous behavior of the height fluctuation width in the
crossover from random to coherent growths of surface for a stochastic model. In
the model, random numbers are assigned on perimeter sites of surface,
representing pinning strengths of disordered media. At each time, surface is
advanced at the site having minimum pinning strength in a random subset of
system rather than having global minimum. The subset is composed of a randomly
selected site and its (ββ1) neighbors. The height fluctuation width
W2(L;β) exhibits the non-monotonic behavior with β and it has a
minimum at ββ. It is found numerically that ββ scales as
βββΌL0.59, and the height fluctuation width at that minimum,
W2(L;ββ), scales as βΌL0.85 in 1+1 dimensions. It is found that
the subset-size ββ(L) is the characteristic size of the crossover from
the random surface growth in the KPZ universality, to the coherent surface
growth in the directed percolation universality.Comment: 13 postscript file