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Scaling limits for planar aggregation with subcritical fluctuations

Published version
Peer-reviewed

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Authors

Norris, James 
Silvestri, Vittoria 

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 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.

Description

Keywords

Primary 60Fxx, Secondary 30C35, 60H15, 60K35, 82C24

Journal Title

PROBABILITY THEORY AND RELATED FIELDS

Conference Name

Journal ISSN

0178-8051
1432-2064

Volume Title

185

Publisher

Springer Science and Business Media LLC