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Scaling limits for planar aggregation with subcritical fluctuations

Research output: Contribution to journalJournal article

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<mark>Journal publication date</mark>4/02/2019
<mark>Journal</mark>arxiv.org
Number of pages51
Publication statusPublished
Original languageEnglish

Abstract

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.

Bibliographic note

51 pages, 7 figures