Multifractal Structure of the Harmonic Measure of Diffusion Limited Aggregates

Details Multifractal Structure of the Harmonic Measure of Diffusion Limited Aggregates Multifractal Structure of the Harmonic Measure of Diffusion Limited Aggregates

2001-10-10

arxiv.org/abs/cond-mat/0110203v1

Physics

Condensed Matter

Statistical Mechanics

submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.65.046109

The method of iterated conformal maps allows to study the harmonic measure of Diffusion Limited Aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of the measure in the deepest fjords that were hitherto screened away from any numerical probing. We resolve probabilities as small as $10^{-35}$, and present an accurate determination of the generalized dimensions and the spectrum of singularities. We show that the generalized dimensions $D_q$ are infinite for $q

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