# Mathematics Colloquia and Seminars

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### The limiting shape of the rotor-router and related models

**Mathematical Physics & Probability**

Speaker: | Lionel Levine, University of California (Berkeley) |

Location: | 0 MSB |

Start time: | Tue, Mar 7 2006, 3:00PM |

The rotor-router model is a deterministic analogue of random walk invented by Jim Propp. It is a close relative of the abelian sandpile and displays much of the same self-organized criticality. I will describe recent work showing that the asymptotic shape of the rotor-router aggregation model is a Euclidean ball in all dimensions. I'll also describe a new model, the divisible sandpile, which motivates a key step in the proof. Finally, I will mention some conjectures concerning non-circular limiting shapes. Joint work with Yuval Peres.