1998/12/14 by Benny Davidovich, Davidovich, Benny, H. G. E. Hentschel +10
Computer Science · Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topological and Geometric Data Analysis #chao-dyn #cond-mat.stat-mech #nlin.CD
paper · pdf · doi:10.48550/arxiv.chao-dyn/9812020
10 pages, 9 figures, Phys. Rev. E, Jan 1st 1999
arxiv created 1998/12/14 · openalex publication_date 1998/12/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The creation of fractal clusters by diffusion limited aggregation (DLA) is studied by using iterated stochastic conformal maps following the method proposed recently by Hastings and Levitov. The object of interest is the function Φ(n) which conformally maps the exterior of the unit circle to the exterior of an n-particle DLA. The map Φ(n) is obtained from n stochastic iterations of a function ϕ that maps the unit circle to the unit circle with a bump. The scaling properties usually studied in the literature on DLA appear in a new light using this language. The dimension of the cluster is determined by the linear coefficient in the Laurent expansion of Φ(n), which asymptotically becomes a deterministic function of n. We find new relationships between the generalized dimensions of the harmonic measure and the scaling behavior of the Laurent coefficients.