Stochastic flows, panar aggregation and the Brownian web

Diffusion limited aggregation (DLA) is a random growth model which was

originally introduced in 1981 by Witten and Sander. This model is prevalent in

nature and has many applications in the physical sciences as well as industrial

processes. Unfortunately it is notoriously difficult to understand, and only one

rigorous result has been proved in the last 25 years. We consider a simplified

version of DLA known as the Eden model which can be used to describe the growth

of cancer cells, and show that under certain scaling conditions this model gives

rise to a limit object known as the Brownian web.