TY - JOUR

T1 - Singular scaling limits in a planar random growth model

AU - Turner, Amanda

PY - 2019/1/4

Y1 - 2019/1/4

N2 - Planar random growth processes occur widely in the physical world. Examplesinclude diffusion-limited aggregation (DLA) for mineral deposition and the Edenmodel for biological cell growth. One of the curious features of these models isthat although the models are constructed in an isotropic way, scaling limits appearto be anisotropic. In this talk, we construct a family of models in which randomlygrowing clusters can be represented as compositions of conformal mappings. Weare able to show rigorously that for certain parameter choices, the scaling limitsare anisotropic and we obtain shape theorems in this case. This contrasts withearlier work on related growth models in which the scaling limits are shown to begrowing disks.

AB - Planar random growth processes occur widely in the physical world. Examplesinclude diffusion-limited aggregation (DLA) for mineral deposition and the Edenmodel for biological cell growth. One of the curious features of these models isthat although the models are constructed in an isotropic way, scaling limits appearto be anisotropic. In this talk, we construct a family of models in which randomlygrowing clusters can be represented as compositions of conformal mappings. Weare able to show rigorously that for certain parameter choices, the scaling limitsare anisotropic and we obtain shape theorems in this case. This contrasts withearlier work on related growth models in which the scaling limits are shown to begrowing disks.

U2 - 10.4171/OWR/2018/4

DO - 10.4171/OWR/2018/4

M3 - Journal article

VL - 15

SP - 235

EP - 238

JO - Oberwolfach Reports

JF - Oberwolfach Reports

SN - 1660-8933

IS - 1

ER -