Scaling limits of anisotropic Hastings-Levitov clusters
2012 (English)In: Annales de l'I.H.P. Probabilites et statistiques, ISSN 0246-0203, Vol. 48, no 1, 235-257 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2012. Vol. 48, no 1, 235-257 p.
Anisotropic growth models, Scaling limits, Loewner differential equation, Boundary flow
IdentifiersURN: urn:nbn:se:kth:diva-12363DOI: 10.1214/10-AIHP395ISI: 000300338800009OAI: oai:DiVA.org:kth-12363DiVA: diva2:309997
QC 20100618. Updated from submitted to published 201203272010-04-122010-04-122012-03-27Bibliographically approved