Skip to main content
Article thumbnail
Location of Repository

The harmonic measure of diffusion-limited aggregates including rare events

By D. A. Adams, Leonard M. (Leonard Michael) Sander, Ellák Somfai and R. M. Ziff


We obtain the harmonic measure of diffusion-limited aggregate (DLA) clusters using a biased random-walk sampling technique which allows us to measure probabilities of random walkers hitting sections of clusters with unprecedented accuracy; our results include probabilities as small as 10- 80. We find the multifractal D(q) spectrum including regions of small and negative q. Our algorithm allows us to obtain the harmonic measure for clusters more than an order of magnitude larger than those achieved using the method of iterative conformal maps, which is the previous best method. We find a phase transition in the singularity spectrum f(α) at α≈14 and also find a minimum q of D(q), qmin=0.9±0.05

Topics: QC
Publisher: EDP Sciences
Year: 2009
OAI identifier:

Suggested articles


  1. (2008). B e l i k o vA . ,G r u z b e r gI .A .and Rushkin I.,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.