Multifractal dimensions and their fluctuations in diffusion-limited aggregation

We use a recently developed a priori theory of diffusion-limited aggregation (DLA) to compute multifractal dimensions and their fluctuations, using methods analogous to field theoretical resummations. There are two regimes, depending upon n, the number of particles in the DLA cluster, as well as on the multifractal moment q. In the strongly fluctuating regime quenched and annealed dimensions differ, while in the weakly fluctuating one they are identical. Our values for multifractal dimensions are in good agreement with numerical results.