Scaling limits of anisotropic Hastings-Levitov clusters
Probability
2012-03-12 v1 Mathematical Physics
Complex Variables
math.MP
Abstract
We consider a variation of the standard Hastings-Levitov model HL(0), in which growth is anisotropic. Two natural scaling limits are established and we give precise descriptions of the effects of the anisotropy. We show that the limit shapes can be realised as Loewner hulls and that the evolution of harmonic measure on the cluster boundary can be described by the solution to a deterministic ordinary differential equation related to the Loewner equation. We also characterise the stochastic fluctuations around the deterministic limit flow.
Keywords
Cite
@article{arxiv.0908.0086,
title = {Scaling limits of anisotropic Hastings-Levitov clusters},
author = {Fredrik Johansson and Alan Sola and Amanda Turner},
journal= {arXiv preprint arXiv:0908.0086},
year = {2012}
}
Comments
31 pages, 5 figures