Abstract: We study regularized versions of the Hastings-Levitov model of Laplacian random growth, and related conformal aggregation models. In addition to the usual feedback parameter alpha>0, such regularized models feature 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, for certain ranges of smoothing parameters. We also study scaling limits of harmonic measure flows on the boundary, and show that it can be described in terms of stopped Brownian webs on the circle. This reports on joint work with Amanda Turner (Lancaster) and Fredrik Viklund (KTH).
Host: John McCarthy