Scaling limits for planar aggregation with subcritical fluctuations

Norris, James and Silvestri, Vittoria and Turner, Amanda (2022) Scaling limits for planar aggregation with subcritical fluctuations. Probability Theory and Related Fields. 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 attachment point of each successive particle is distributed according to 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.

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Journal Article
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Probability Theory and Related Fields
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01 Jun 2022 14:50
Last Modified:
22 Nov 2022 07:03