Abstract. We consider a variation of the standard HastingsLevitov 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.
Recently, Johansson Viklund, Sola and Turner REF studied an anisotropic version of the Hastings-Levitov model in the α = 0 case, and established deterministic scaling limits for the macroscopic shape and evolution of harmonic measure on the cluster boundary.
Scaling limits of anisotropic Hastings-Levitov clusters
Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques 2012, Vol. 48, No. 1, 235-257
Mathematics Physics