Playlist - Planar random growth and scaling limits

Conformal growth models are motivated by some real-world growth processes, and are constructed using conformal maps. We will introduce the one-parameter Hastings–Levitov model, which is used to describe Laplacian growth and allows us to vary between off-lattice versions of many well studied models. Then we investigate the "small particle" scaling limit, which often entails finding a martingale and relating its behaviour to its analogue for the proposed continuum limit.

Conformal growth models are motivated by some real-world growth processes, and are constructed using conformal maps. We will introduce the one-parameter Hastings–Levitov model, which is used to describe Laplacian growth and allows us to vary between off-lattice versions of many well studied models. Then we investigate the "small particle" scaling limit, which often entails finding a martingale and relating its behaviour to its analogue for the proposed continuum limit.