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Scaling limits of anisotropic Hastings-Levitov clusters.

Johansson Viklund, Fredrik and Sola, Alan and Turner, Amanda (2012) Scaling limits of anisotropic Hastings-Levitov clusters. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 48 (1). pp. 235-257.

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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.

Item Type: Article
Journal or Publication Title: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Uncontrolled Keywords: Anisotropic growth models ; Scaling limits ; Loewner differential equation ; Boundary flow
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 26869
Deposited By: Dr Amanda Turner
Deposited On: 04 Aug 2009 10:29
Refereed?: Yes
Published?: Published
Last Modified: 09 Apr 2014 20:29
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/26869

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