Kaj Börjesson: Internal Diffusion Limited Aggregation and obstacle

We study the stochastic growth model known as Internal DLA which is a growth model in Z^d.

It features a cluster determined by adding new particles according to random walks.

A particle travels from inside the cluster and stops when reaching the first point outside the region, adding that point to the region. We are mainly interested in the asymptotics of the occupied sets and present how this relates to PDE theory, in particular the obstacle problem and the Stefan problem.

We also discuss some related models, the Divisible Sandpile, Rotor-Router Aggregation and the Classical Sandpile.