Small-particle limits in regularized Laplacian growth models

by Alan Sola (Mathematics Department SU)

Wednesday 15 Mar 2017, 11:00 → 12:00 Europe/Stockholm

A4:1069

We study a regularized version of the Hastings-Levitov 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. Joint work with Amanda Turner and Fredrik Viklund.