A renormalisation group method is presented to analyse the scaling structure of the growth probability in diffusion-limited aggregation. The recursion relation for the growth probability is derived under the renormalisation transformation. The growth probability assigned to each growth bond is represented by a random multiplicative process. The scaling of the highest growth probability is derived and the fractal dimension is found. A hierarchy of generalised dimensions D(q) is calculated to describe the growth probability. The partition of (q-1)D(q) into a density of singularities f(q) with singularity strength alpha (q) is made and the alpha -f spectrums are found.
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Takashi Nagatani (1987) studied this question.