We present a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions. Key steps are understanding how these models interrelate when the ultra-violet cut-off strategy is changed, the analogy with turbulence and the use of logarithmic field variables. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is both predicted and confirmed.
@article{arxiv.cond-mat/0205660,
title = {Theory of Diffusion Controlled Growth},
author = {R. C. Ball and E. Somfai},
journal= {arXiv preprint arXiv:cond-mat/0205660},
year = {2007}
}