Aggregation in the Plane and Loewner's Equation

By L. Carleson, N. Makarov. 2001

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Conformally invariant scaling limits: an overview and a collection of problems (2006, methodology): “) Makarov and Carleson [22] used Loewner’s equation to study a much simplified deterministic variant of DLA, which is not fractal, and Hastings and Levitov [34] have used conformal mapping techniques for a non-rigorous study of more realistic versions of DLA.”
The evolution of Loewner's differential equations (2010, methodology): “Makarov [13], studying growth processes motivated by DLA (diffusion-limited aggregation) via Loewner’s equations.”
Random planar curves and Schramm-Loewner evolutions (2003, methodology): “Carleson and Makarov [35, 36] have used Loewner’s (radial) equation in the context of Diffusion Limited Aggregation.”
Laplacian path models (2002, background): “Also see [4] for a general discussion of the role of Loewner’s equation in aggregation models.”