Statistics Seminars: Scaling limits of Laplacian random growth models
16 January 2017 14:00 in CM221
The idea of using conformal mappings to represent randomly growing clusters has been around for almost 20 years. Examples include the Hastings-Levitov models for planar random growth, which cover physically occurring processes such as diffusion-limited aggregation (DLA), dielectric breakdown and the Eden model for biological cell growth, and more recently Miller and Sheffield's Quantum Loewner Evolution (QLE). In this talk we will discuss ongoing work on a natural variation of the Hastings-Levitov family. For this model, we are able to prove that both singular and absolutely continuous scaling limits can occur. Specifically, we can show that for certain parameter values, under a sufficiently weak regularisation, the resulting cluster can be shown to converge to a randomly oriented one-dimensional slit, whereas under sufficiently strong regularisations, the scaling limit is a deterministically growing disk.
This is based on work in progress with Alan Sola (Stockholm) and Fredrik Viklund (KTH).
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