PERSISTENCE OF SCREENING AND SELF-CRITICALITY IN THE SCALE-INVARIANT DYNAMICS OF DIFFUSION-LIMITED AGGREGATION

The origin of fractal properties in diffusion limited aggregation is r elated to the persistence of screening in the scale invariant growth r egime. This effect is described by the effective noise reduction param eter S spontaneously generated by the scale invariant dynamics. The re normalization of this parameter under scale transformation shows the f ollowing: (i) The fixed point is attractive, implying the self-critica l nature of the process. (ii) The fixed point value S is of the order of unity, showing that the small scale growth rules are already close to the scale invariant ones and that screening effects persist in the asymptotic regime.