The Harmonic Measure of Diffusion-Limited Aggregates including Rare Events

Abstract

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(alpha) at alpha approximately equal to 14 and also find a minimum q of D(q), q_{min} = 0.9 plus or minus 0.05.

11 pages, 5 figures

References in corpus (6)

• Stochastic geometry of critical curves, Schramm-Loewner evolutions, and conformal field theory
• Diffusion-limited aggregation in channel geometry
• Harmonic Measure for Percolation and Ising Clusters Including Rare Events
• Harmonic measure and winding of random conformal paths: A Coulomb gas perspective
• Finite size effect of harmonic measure estimation in a DLA model: Variable size of probe particles
• Statistics of harmonic measure and winding of critical curves from conformal field theory

Cited by in corpus (7)

• The Barrier Method: A Technique for Calculating Very Long Transition Times
• Scaling laws in the diffusion limited aggregation of persistent random walkers
• How anisotropy beats fractality in two-dimensional on-lattice DLA growth
• Effects of target anisotropy on harmonic measure and mean first-passage time
• First-passage times to a fractal boundary: local persistence exponent and its log-periodic oscillations
• The Harmonic Measure for critical Potts clusters
• Stationary growth and unique invariant harmonic measure of cylindrical DLA