Small-particle limits in regularized Laplacian growth models
KTH/Nordita/SU seminar in Theoretical Physics
Wednesday 15 March 2017
to 12:00 at
Alan Sola (Mathematics Department SU)
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.