Small-particle limits in a regularized Laplacian random growth model

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• Turner, A (Lancaster University)
• Tuesday 17 March 2015, 14:00-15:00
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact Mustapha Amrani.

Random Geometry

Co-authors: Fredrik Johansson Viklund (Uppsala University), Alan Sola (University of Cambridge)

In 1998 Hastings and Levitov proposed a one-parameter family of models for planar random growth in which clusters are represented as compositions of conformal mappings. This family includes physically occurring processes such as diffusion-limited aggregation (DLA), dielectric breakdown and the Eden model for biological cell growth. In the simplest case of the model (corresponding to the parameter alpha=0), James Norris and I showed how the Brownian web arises in the limit resulting from small particle size and rapid aggregation. In particular this implies that beyond a certain time, all newly aggregating particles share a single common ancestor. I shall show how small changes in alpha result in the emergence of branching structures within the model so that, beyond a certain time, the number of common ancestors is a random number whose distribution can be obtained. This is based on joint work with Fredrik Johansson Viklund (Uppsala) and Alan Sola (Cambridge).

This talk is part of the Isaac Newton Institute Seminar Series series.

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