  Domain walls, optimal droplets and disorder chaos at zero temperature are
studied numerically for the solid-on-solid model on a random substrate. It is
shown that the ensemble of random curves represented by the domain walls obeys
Schramm's left passage formula with kappa=4 whereas their fractal dimension is
d_s=1.25, and therefore is NOT described by "Stochastic-Loewner-Evolution"
(SLE). Optimal droplets with a lateral size between L and 2L have the same
fractal dimension as domain walls but an energy that saturates at a value of
order O(1) for L->infinity such that arbitrarily large excitations exist which
cost only a small amount of energy. Finally it is demonstrated that the
sensitivity of the ground state to small changes of order delta in the disorder
is subtle: beyond a cross-over length scale L_delta ~ 1/delta the correlations
of the perturbed ground state with the unperturbed ground state, rescaled by
the roughness, are suppressed and approach zero logarithmically.
