Theory of diffusion-limited growth

We review and extend the field-theoretic approach to diffusion-limited growth at a finite background walker density. This approach leads to an Ito-type stochastic evolution equation with a multiplicative noise term. We show that a consistent mean-field (i.e., deterministic) reduction of this problem contains an unexpected low-density cutoff induced by the net probability drift due to the aforementioned noise. At the conclusion, implications of these findings for a first-principles theory of diffusion-limited-aggregation fractals are discussed.