Scaling limits of random growth processes

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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 approach to mathematically modelling such processes is to represent the randomly growing clusters as compositions of conformal mappings. In 1998, Hastings and Levitov proposed one such family of models, which includes versions of the physical processes described above. In earlier work, Norris and Turner showed that the scaling limit of the simplest of the Hastings-Levitov models is a growing disk in the small-particle limit. This is the limit in which the capacity of each particle tends to zero while the number of particles is tuned so that the total capacity of the cluster remains constant. This PhD project will instead aim to obtain scaling limits in the limit where the whole cluster is rescaled by its total capacity.