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.