Alan Sola: One dimensional scaling limits in a Laplacian random growth model
Tid: On 2019-10-16 kl 13.15 - 14.15
Plats: F11, KTH
Medverkande: Alan Sola, Stockholms universitet
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.