Scaling limits for planar aggregation with subcritical fluctuations

Norris, James and Silvestri, Vittoria and Turner, Amanda (2023) Scaling limits for planar aggregation with subcritical fluctuations. Probability Theory and Related Fields, 185 (1-2). pp. 185-250. ISSN 0178-8051

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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.

Item Type:
Journal Article
Journal or Publication Title:
Probability Theory and Related Fields
Uncontrolled Keywords:
?? math.prmath-phmath.cvmath.mpanalysisstatistics and probabilitystatistics, probability and uncertainty ??
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Deposited On:
01 Jun 2022 14:50
Last Modified:
22 May 2024 00:48