TY - JOUR

T1 - Scaling limits of anisotropic Hastings-Levitov clusters.

AU - Johansson Viklund, Fredrik

AU - Sola, Alan

AU - Turner, Amanda

PY - 2012/2/6

Y1 - 2012/2/6

N2 - 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.

AB - 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.

KW - Anisotropic growth models

KW - Scaling limits

KW - Loewner differential equation

KW - Boundary flow

U2 - 10.1214/10-AIHP395

DO - 10.1214/10-AIHP395

M3 - Journal article

VL - 48

SP - 235

EP - 257

JO - Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

JF - Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

IS - 1

ER -