We report the results of numerical investigations of the steady-state (SS)
and finite-initial-conditions (FIC) spatial persistence and survival
probabilities for (1+1)--dimensional interfaces with dynamics governed by the
nonlinear Kardar--Parisi--Zhang (KPZ) equation and the linear
Edwards--Wilkinson (EW) equation with both white (uncorrelated) and colored
(spatially correlated) noise. We study the effects of a finite sampling
distance on the measured spatial persistence probability and show that both SS
and FIC persistence probabilities exhibit simple scaling behavior as a function
of the system size and the sampling distance. Analytical expressions for the
exponents associated with the power-law decay of SS and FIC spatial persistence
probabilities of the EW equation with power-law correlated noise are
established and numerically verified.Comment: 11 pages, 5 figure