Scaling limits of anisotropic Hastings-Levitov clusters

Details Scaling limits of anisotropic Hastings-Levitov clusters Scaling limits of anisotropic Hastings-Levitov clusters

2009-08-03

arxiv.org/abs/0908.0086v1

Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques 2012, Vol. 48, No. 1, 235-257

Mathematics

Probability

31 pages, 5 figures

Scientific paper

10.1214/10-AIHP395

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.

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