Renormalisation group for DLA and fixed-point distribution
- 1 December 1987
- journal article
- editorial
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 20 (17) , 6135-6141
- https://doi.org/10.1088/0305-4470/20/17/047
Abstract
A renormalization group method is presented to analyse the multifractal structure of the growth probability in the diffusion-limited aggregation (DLA). A renormalisation group transformation is derived for the probability distribution of the growth bond's conductance. After repeated scaling, an 'invariant' distribution is reached as a fixed-point distribution. The growth probability assigned to each growth bond is represented by a random multiplicative process of the cell's growth probability with fixed-point distribution. A hierarchy of generalised dimensions D(q) is calculated and the alpha -f spectrum is found.Keywords
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