## Conformal theory of the dimensions of diffusion-limited aggregates

### Abstract

We employ the recently introduced conformal iterative construction of Diffusion-Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process which is complementary to the iterative cluster growth. We use this method to establish the existence of a series of random scaling functions that yield, via the thermodynamic formalism of multifractals, the generalized dimensions Dq of DLA for $q\ge 1$. The scaling function is determined just by the last stages of the iterative growth process 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 $D_0=1.69\pm 0.03$

Publisher: 'IOP Publishing'
Year: 2002
DOI identifier: 10.1209/epl/i1999-00518-y
OAI identifier: oai:edpsciences.org:dkey/10.1209/epl/i1999-00518-y