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One-Dimensional Scaling Limits in a Planar Laplacian Random Growth Model
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 32019 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 371, no 1, p. 285-329Article in journal (Refereed) Published
Abstract [en]

We consider a family of growth models defined using conformal maps in which the local growth rate is determined by |phi n '|-eta where phi n is the aggregate map for n particles. We establish a scaling limit result in which strong feedback in the growth rule leads to one-dimensional limits in the form of straight slits. More precisely, we exhibit a phase transition in the ancestral structure of the growing clusters: for eta>1aggregating particles attach to their immediate predecessors with high probability, while for eta<1almost surely this does not happen.

Place, publisher, year, edition, pages
2019. Vol. 371, no 1, p. 285-329
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-175858DOI: 10.1007/s00220-019-03460-1ISI: 000488928900009OAI: oai:DiVA.org:su-175858DiVA, id: diva2:1369258
Available from: 2019-11-11 Created: 2019-11-11 Last updated: 2019-11-11Bibliographically approved

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