Renormalization Theory of Stochastic Growth
Matthew B. Hastings
TL;DR
This paper develops a renormalization group approach to analyze stochastic growth models like DLA, accurately computing fractal and multifractal properties, and suggesting broader applicability to related phenomena.
Contribution
It introduces an analytical renormalization group method for stochastic growth, providing precise calculations of fractal dimensions and multifractal exponents for DLA.
Findings
Fractal dimension of DLA computed as 1.7.
Multifractal exponents match numerical results.
Potential extension to dielectric breakdown model.
Abstract
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.
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