Researchers: Anne Schreuder, Ilya Losev, James Norris

In this project we study two-dimensional particle growth models. These models are defined iteratively. Starting from a seed particle we attach another particle to its boundary via a prescribed probability measure. Examples include the uniform measure on the boundary or harmonic measure. In each further step we attach another particle to the boundary of the current particle collection. Motivation to look at these kind of models comes from the physical sciences as well as biology where fractal-like growth has been observed in different contexts. Depending on the chosen model parameters these models are used to describe for instance growth of bacterial colonies, electrodeposition, disposition of materials and the dielectric breakdown. The goal of this project is to describe the limit shapes of these processes as well as to understand universality classes, i.e. classes of models which share the same scaling limit.