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 related to the persistence of screening in the scale invariant growth regime. This effect is described by the effective noise reduction parameter S spontaneously generated by the scale invariant dynamics. The renormalization of this parameter under scale transformation shows the following: (i) The fixed point is attractive, implying the self-critical nature of the process. (ii) The fixed point value ${\mathit{S}}^{\mathrm{*}}$ 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 persisit in the asympotic regime.