Random Aggregation on the Complex Plane and the Hastings-Levitov Models

Explore the fascinating world of random aggregation on the complex plane in this 50-minute lecture presented by Vittoria Silvestri from Sapienza University of Rome. Delve into the Aggregate Loewner Evolution (ALE) models, which describe growing random clusters through iterated composition of random conformal maps. Discover how these models serve as off-lattice analogues for fundamental discrete models like Eden growth, Dielectric Breakdown, and Diffusion Limited Aggregation. Examine the large-scale properties of ALE models, including Hastings-Levitov models, focusing on scaling limits and fluctuations. Gain insights into current conjectures and open questions in this field, based on collaborative research with James Norris and Amanda Turner. Recorded as part of IPAM's Statistical Mechanics Beyond 2D Workshop, this talk offers a comprehensive overview of random aggregation processes and their mathematical implications.