Diffusion-Limited Aggregation as Branched Growth

I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys. Rev. A 46, 7793 (1992)]. This leads to a result for the cluster dimensionality, D ≍ 1.66, which is close to numerically obtained values. Quenched and annealed multifractal dimensions can also be computed in this theory; the multifractal dimension τ(3) = D, in agreement with a proposed “electro-static” scaling law.