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Scaling Limits for Planar Aggregation with Subcritical Fluctuations by Norris, James; Silvestri, Vittoria; Turner, Amanda is a scholarly article available to read on EtoBox.

What is Scaling Limits for Planar Aggregation with Subcritical Fluctuations about?

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.

Author

Norris, James; Silvestri, Vittoria; Turner, Amanda

Published

2019

Language

EN