Diffusion-limited aggregation

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Abstract
Diffusion-limited aggregation (DLA) is an idealization of the process by which matter irreversibly combines to form dust, soot, dendrites, and other random objects in the case where the rate-limiting step is diffusion of matter to the aggregate. We study the process from several points of view stressing the fact that it apparently gives rise to scale-invariant objects whose Hausdorff dimension is independent of short-range details. We show that DLA has no upper critical dimension. We apply scale invariance to study growth, gelation, and the structure factor of aggregates.