Title: Spherical asymptotics for the rotor-router model in $\mathbb{Z}^d$

Authors: Lionel Levine and Yuval Peres

Issue: Volume 57 (2008), Issue 1, 431-450

Abstract: The rotor-router model is a deterministic analogue of random walk invented by Jim Propp. It can be used to define a deterministic aggregation model analogous to internal diffusion limited aggregation. We prove an isoperimetric inequality for the exit time of simple random walk from a finite region in $\mathbb{Z}^d$, and use this to prove that the shape of the rotor-router aggregation model in $\mathbb{Z}^d$, suitably rescaled, converges to a Euclidean ball in $\mathbb{R}^d$.