Renormalization Theory of Stochastic Growth

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.

39 pages, LaTeX, 11 figures

References in corpus (2)

• Diffusion-limited aggregation as branched growth
• Observation of Conservations Laws in Diffusion Limited Aggregation

Cited by in corpus (16)

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• Iterated Conformal Dynamics and Laplacian Growth
• The branching structure of diffusion-limited aggregates
• Finite size effect of harmonic measure estimation in a DLA model: Variable size of probe particles
• Anisotropic Diffusion Limited Aggregation
• The Average Shape of Transport-Limited Aggregates
• Variable size particle probing of the DLA cluster properties
• Diffusion limited aggregation as a Markovian process: site-sticking conditions
• Diffusion limited aggregation as a Markovian process. Part I: bond-sticking conditions
• Fractal Structure of Hastings-Levitov Patterns Restricted in a Sector Geometry
• The fractal dimensions of Laplacian growth: an analytical approach based on a universal dimensionality function
• Diffusion Limited Aggregation with Power-Law Pinning