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Scaling limits of anisotropic Hastings-Levitov clusters.

Research output: Contribution to journalJournal article

Published

Journal publication date6/02/2012
JournalAnnales de L'Institut Henri Poincaré (B) Probabilités et Statistiques
Journal number1
Volume48
Number of pages23
Pages235-257
Early online date23/01/12
Original languageEnglish

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.