LOCALIZATION OF FRACTONS, RANDOM-WALKS AND LINEAR-POLYMERS IN PERCOLATION

We review analytical and numerical results for the vibrational amplitu des of localized excitations, the probability distribution of random w alks and the distribution of linear polymers (modeled by self-avoiding walks of N steps) on percolation structures at criticality. Our numer ical results show that the fluctuations of these quantities, at fixed shortest-path distance (''chemical length'') l from the center of loca lization, are considerably smaller than at fixed Euclidean distance r from the center. Using this fact, we derive via convolutional integral s explicit expressions for the averaged functions in r-space, and show analytically and numerically that three different localization regime s occur. In the short-distance regime, remarkably, the averages show a universal spatial decay behavior, with the same exponent for both fra ctons and random walks, while in the asymptotic regime, the averages d epend explicitly on the number of configurations considered.