Spherical asymptotics for the rotor-router model in Zd

@article{Levine2005SphericalAF,
  title={Spherical asymptotics for the rotor-router model in Zd},
  author={Lionel Levine and Yuval Peres},
  journal={Indiana University Mathematics Journal},
  year={2005},
  volume={57},
  pages={431-450}
}
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 Z d , and use this to prove that the shape of the rotor-router aggregation model in Z d , suitably rescaled, converges to a Euclidean ball in R d . 

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