Wednesday, 26 March, 2014
SPEAKER: Prof. Alan Sola, Cambridge UK
TITLE: Scaling limits in a regularized Laplacian growth model
ABSTRACT: I will report on joint work with F. Viklund (Uppsala) and A. Turner (Lancaster) on a regularized version of the Hastings-Levitov conformal mapping model of Laplacian random growth. In addition to the usual feedback parameter $alpha>0$, this regularized version features a smoothing parameter $sigma>0$.
We prove convergence of random clusters, in the limit as the size of the individual aggregating particles tends to zero, to deterministic limits, provided the smoothing parameter does not tend to zero too fast. We also
study scaling limits of the harmonic measure flow on the boundary, and show that it can be described in terms of stopped Brownian webs on the circle.