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Scaling limits for planar aggregation with subcritical fluctuations

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>28/02/2023
<mark>Journal</mark>Probability Theory and Related Fields
Issue number1-2
Number of pages66
Pages (from-to)185-250
Publication StatusPublished
Early online date11/06/22
<mark>Original language</mark>English


We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. We show that, when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that as the power approaches the edge of this range the fluctuations approach a critical point, which is a limit of stability. The methodology developed in this paper provides a blueprint for analysing more general random growth models, such as the Hastings-Levitov family.