Renormalization Theory of Stochastic Growth

An analytical renormalization group treatment is presented of a model which, for one value of parameters, is equivalent to diffusion limited aggregation. The fractal dimension of DLA is computed to be 2-1/2+1/5=1.7. Higher multifractal exponents are also calculated and found in agreement with numerical results. It may be possible to use this technique to describe the dielectric breakdown model as well, which is given by different parameter values.Comment: 39 pages, LaTeX, 11 figure