Universiteit Utrecht

Department of Mathematics

Internal Diffusion Limited Aggregation

Wouter Kager

11 March 2009

Internal Diffusion Limited Aggregation (IDLA) is a model in which an aggregate of particles is gradually expanded by the following rule: at each stage of the growth, an independent random walker starts in the origin of the lattice and drops a new particle at the first unoccupied site it encounters. The central question is what the cluster of dropped particles looks like in the long run. In particular, does it assume a (deterministic) limit shape? The answer will depend on the random walk used in the model. In this talk, I will discuss joint work with Lionel Levine on a family of IDLA models in two dimensions for which the limit shape is a diamond.

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Alexandra Babenko