1998/12/20 by Benny Davidovich, Itamar Procaccia · 7 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Conformal map #Dimension (graph theory) #Formalism (music) #Fractal #Fractal dimension #Geometry #Harmonic function #Harmonic measure #Mathematical analysis #Mathematics #Multifractal system #Physics #Pure mathematics #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #chao-dyn #cond-mat.stat-mech #nlin.CD
paper · pdf · doi:10.1209/epl/i1999-00518-y
published in Europhysics Letters (EPL) 48(5), 547-553 (Institute of Physics) · 5 pages, 3 figures, submitted to Phys. Rev. Lett
arxiv created 1998/12/20 · openalex publication_date 1999/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We employ the recently introduced conformal iterative construction of Diffusion-Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process which is complementary to the iterative cluster growth. We use this method to establish the existence of a series of random scaling functions that yield, via the thermodynamic formalism of multifractals, the generalized dimensions D q of DLA for q ⩾ 1. The scaling function is determined just by the last stages of the iterative growth process which are relevant to the complementary dynamics. Using the scaling relation D 3 = D 0 /2, we estimate the fractal dimension of DLA to be D 0 = 1.69 ± 0.03.