Singular scaling limits in a planar random growth model

Turner, Amanda (2019) Singular scaling limits in a planar random growth model. Oberwolfach Reports, 15 (1). pp. 235-238. ISSN 1660-8933

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Planar random growth processes occur widely in the physical world. Examples include diffusion-limited aggregation (DLA) for mineral deposition and the Eden model for biological cell growth. One of the curious features of these models is that although the models are constructed in an isotropic way, scaling limits appear to be anisotropic. In this talk, we construct a family of models in which randomly growing clusters can be represented as compositions of conformal mappings. We are able to show rigorously that for certain parameter choices, the scaling limits are anisotropic and we obtain shape theorems in this case. This contrasts with earlier work on related growth models in which the scaling limits are shown to be growing disks.

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Journal Article
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Oberwolfach Reports
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Deposited On:
07 May 2019 10:25
Last Modified:
20 Sep 2023 01:22