Scaling limits of anisotropic Hastings-Levitov clusters

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.

31 pages, 5 figures

References in corpus (4)

• The Brownian web: Characterization and convergence
• Laplacian growth as one-dimensional turbulence
• Weak convergence of the localized disturbance flow to the coalescing Brownian flow
• Anisotropic Diffusion Limited Aggregation

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