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Analysis and PDE Seminar

Date:
-
Location:
745 Patterson Office Tower
Speaker(s) / Presenter(s):
Dr. Alan Sola, University of Cambridge

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 $\sigma>0$.

Using coupling arguments and continuity properties of the Loewner PDE, 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.