# Alan Sola: One dimensional scaling limits in a Laplacian random growth model

Time: Wed 2019-10-16 13.15 - 14.15

Lecturer: Alan Sola, Stockholms universitet

Location:

### Abstract

In joint work with A. Turner and F. Viklund, we consider growth models defined using conformal maps in which local growth is determined by $$|\Phi_n'|^{-\eta}$$, where $$\Phi_n$$ is the aggregate map for $$n$$ particles. We establish a scaling limit result in which

strong feedback in the growth rule leads to one-dimensional limits in the form of straight slits. More precisely, we exhibit a phase transition in the ancestral structure: for $$\eta>1$$, aggregating particles attach to their immediate predecessors with high probability, while for $$\eta<1$$ there is a positive probability that this does not happen.

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Last changed: Oct 03, 2019