Title: “Planar aggregation with subcritical fluctuations and the Hastings-Levitov models”.

Abstract: The ALE (Aggregate Loewner Evolution) models describe growing random clusters on the complex plane, built by iterated composition of random conformal maps. A striking feature of these models is that they can be used to define natural off-lattice analogues of several fundamental discrete models, such as Eden or  Diffusion Limited Aggregation, by tuning the correlation between the defining maps appropriately. In this talk I will discuss shape theorems and fluctuations of ALE clusters, which include Hastings-Levitov clusters as particular cases, in the subcritical regime. Based on joint work with James Norris and Amanda Turner.