SAMPLING-INDUCED HIDDEN CYCLES IN CORRELATED RANDOM ROUGH SURFACES

We show both experimentally and theoretically that the sampling-induce d hidden cycles can exist in scale-invariant rough surfaces having a c orrelation length xi. If the sampling size L is sufficiently large, th e oscillatory behavior will diminish with the fluctuation within an or der of (xi/L)(d/2). This is consistent with the law of large numbers f or the correlated systems: the average of N-correlated variables havin g a correlation length xi will converge to their mean within an order of root xi(d)/N. Based on this result, we propose that in order to dis tinguish the mound surface from the self-affine surface, the sampling condition root xi(d)/N much less than 1 and an average of a large numb er of images are required.