Renormalization theory of stochastic growth

1996/07/01 by Matthew B. Hastings · 4 citations
Economics, Econometrics and Finance · Materials Science · Physics and Astronomy · #Complex Systems and Time Series Analysis #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat

paper · pdf · doi:10.1103/physreve.55.135

39 pages, LaTeX, 11 figures

arxiv created 1996/07/01 · openalex publication_date 1997/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An analytical renormalization-group treatment is presented of a model that, for one value of parameters, is equivalent to diffusion-limited aggregation (DLA). The fractal dimension of DLA is computed to be 2-1/2+1/5=1.7. Higher multifractal exponents are also calculated and found to be 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.

Citations

• Observation of conservations laws in diffusion limited aggregation
• Large-distance and long-time properties of a randomly stirred fluid

Cited by

• Probing surface characteristics of diffusion-limited-aggregation clusters with particles of variable size
• Laplacian growth with separately controlled noise and anisotropy
• Anisotropic diffusion-limited aggregation
• The branching structure of diffusion-limited aggregates