Conformal theory of the dimensions of diffusion-limited aggregates

We employ the recently introduced conformal iterative construction of Diffu sion-Limited Aggregates (DLA) to study the multifractal properties of the h armonic measure. The support of the harmonic measure is obtained from a dyn amical process which is complementary to the iterative cluster growth. We u se this method to establish the existence of a series of random scaling fun ctions that yield, via the thermodynamic formalism of multifractals, the ge neralized dimensions D-q of DLA for q greater than or equal to 1. The scali ng function is determined just by the last stages of the iterative growth p rocess which are relevant to the complementary dynamics. Using the scaling relation D-3 = D-0/2, we estimate the fractal dimension of DLA to be D-0 = 1.69+/-0.03.